35:["$","title",null,{"children":"CAP 4720 Final Project: The Monte Carlo Sampler Group Presentation FINAL ITERATION | Sumant Pattanaik | Observable"}] 3d:T91f,{ const myCanvas = DOM.canvas(canvasWidth, canvasHeight); const gl = regl({ canvas: myCanvas }); gl.clear({ color: [.88, .88, .99, 1] }); for (var i = 0; i < yAxisList.length; i++) gl(generateAxis(yAxisList[i].positions, yAxisList[i].cells))(); for (var i = 0; i < xAxisList.length; i++) gl(generateAxis(xAxisList[i].positions, xAxisList[i].cells))(); var drawPoint; if (algorithmChoice == "Random") { var output = randomPoints(pointSpecs.pointAmount, inputDimensions.width, inputDimensions.height) drawPoint = gl( drawPoints(output.pointList, output.colors, pointWidth)); } else if (algorithmChoice == "Halton") { var haltonContainer = haltonPointsList( pointSpecs.pointAmount, [haltonSpecific.dim1, haltonSpecific.dim2], inputDimensions.width, inputDimensions.height ); drawPoint = gl( drawPoints(haltonContainer.pointList, haltonContainer.colors, pointWidth) ); } else if (algorithmChoice == "Sobol") drawPoint = gl( drawPoints( SobolArray( pointSpecs.pointAmount, inputDimensions.width, inputDimensions.height ), sobolColors, pointSpecs.pointWidth ) ); else if (algorithmChoice == "Hypercube") //drawPoint = gl(drawPoints(lhcPoint(pointSpecs.pointAmount).pointList, sobolColors, pointSpecs.pointWidth)); drawPoint = gl( drawPoints( lhcPoint( pointSpecs.pointAmount, inputDimensions.width, inputDimensions.height ).pointList, sobolColors, pointSpecs.pointWidth ) ); else if (algorithmChoice == "Poisson") { var d = poissonSpecific.minDistance; var poissonArray = poissonPoints( pointSpecs.pointAmount, d, inputDimensions.width, inputDimensions.height ).pointList; var poiColors = poissonColors(poissonArray).colors; drawPoint = gl( drawPoints(poissonArray, poiColors, pointSpecs.pointWidth) ); } else if (algorithmChoice == "pmj02") { var output = pmj02Output( pointSpecs.pointAmount, inputDimensions.width*2, inputDimensions.height*2 ); drawPoint = gl( drawPoints(output.pointList, output.colors, pointSpecs.pointWidth) ); } drawPoint(); return myCanvas; }3e:T5f9,{ const myCanvas = DOM.canvas(500, 500); const gl = regl({ canvas: myCanvas }); gl.clear({ color: [.88, .88, .99, 1] }); var drawShape = gl(testErrorShape(shape)) var drawPoint; var n = numbaOfPoints if (algorithmChoice2 == "Random") drawPoint = gl(drawPoints(randomPoints(n,canvasWidth*2, canvasHeight*2).pointList, randomPoints(n).colors, 3)); else if (algorithmChoice2 == "Halton") drawPoint = gl(drawPoints(haltonPointsList(n, [haltonSpecific2.dim1, haltonSpecific2.dim2],canvasWidth*2, canvasHeight*2).pointList, haltonPointsList(n, [haltonSpecific2.dim1, haltonSpecific2.dim2],canvasWidth*2, canvasHeight*2).colors, 3)); else if (algorithmChoice2 == "Hypercube") drawPoint = gl(drawPoints(lhcPoint(n, canvasWidth*2, canvasHeight*2).pointList, lhcPoint(n).colors, 3)); else if (algorithmChoice2 == "Sobol") drawPoint = gl(drawPoints(SobolArray(n, canvasWidth*2, canvasHeight*2), sobolColors, 3)); else if (algorithmChoice2 == "Poisson") { var d = poissonSpecific.minDistance; var poissonArray = poissonPoints(n, d, canvasWidth*2, canvasHeight*2).pointList var poiColors = poissonColors(poissonArray).colors drawPoint = gl(drawPoints(poissonArray, poiColors, 3)); } else if (algorithmChoice == "pmj02") { var output = pmj02Output( n, canvasWidth*4, canvasHeight*4 ); drawPoint = gl( drawPoints(output.pointList, output.colors, 3) ); } drawPoint(); drawShape(); return myCanvas }3f:Tc98,{ // code modified from https://observablehq.com/@spattana/d3-introducing // on the line graph example let svg = d3.select(DOM.svg(canvasWidth+100,canvasHeight+100)); let chart = svg.append("g").attr("transform",`translate(${50}, ${50})`); let samplers = ["Random", "Halton", "Sobol", "Latin Hypercubes", "Poisson", "PMJ"] let percErrorList = [errorValues.random, errorValues.halton, errorValues.sobol, errorValues.latin, errorValues.poisson, errorValues.pmj] let data = samplers.map((sampler,index)=>({name:sampler, points: errorValues.xval.map( (xval, j)=>({x: xval,y:percErrorList[index][j]}) )})) let xDomain = [0,errorValues.xval[errorValues.xval.length - 1]] let yDomain = [0, 140]; let colorDomain = samplers; let xScale = d3.scaleLinear().domain(xDomain).range([0, canvasWidth]).nice(); let yScale = d3.scaleLinear().domain(yDomain).range([canvasHeight, 0]).nice(); let colorScale = d3.scaleOrdinal().domain(colorDomain).range(d3.schemeCategory10); //axes let xAxis = d3.axisBottom().scale(xScale).ticks(20); let yAxis = d3.axisLeft().scale(yScale).ticks(14, ".0s"); chart.append('g').attr('transform', `translate(0, ${canvasHeight})`).call(xAxis); chart.append('g').call(yAxis) // text label for the x axis chart.append("text") .attr("transform", `translate(${canvasWidth/2},${canvasHeight + 50/1.5})`) .style("text-anchor", "middle") .text("N points"); // text label for the y axis chart.append("text") .attr("transform", "rotate(-90)") .attr("y", 0 - 50) .attr("x",0 - (canvasHeight / 2)) .attr("dy", "1em") .style("text-anchor", "middle") .text("Percent error"); // Create Title const title = svg.append("text") .attr("x", canvasWidth/2 + 100 ) .attr("y", 50/2) .style("font-size", 32) .style("text-anchor", "middle") .text("Error as a function of N points"); // Create lines const line = d3.line() //.defined(d => !isNaN(d.value)) .x(d => xScale(d.x)) .y(d => yScale(d.y)) .curve(d3.curveCardinal); // Draw the lines. svg.append('g') .selectAll('path') .data(data) .join('path') .style("fill", "none") .attr("transform", "translate(50,50)") .style("stroke", (d,i)=>colorScale(samplers[i])) .attr('d', (d) => line(d.points)); // Draw the legend const legend = chart .append('g') .attr('transform', `translate(${canvasWidth - 100},50)`); const labelHeight = 14; legend.selectAll('rect') .data(data) .join('rect') .attr('y', (d,i) => labelHeight * i * 1.8) .attr('width', labelHeight) .attr('height', labelHeight) .attr('fill', d => colorScale(d.name)) .attr('stroke', 'grey') .style('stroke-width', '1px'); legend.selectAll('text') .data(data) .join('text') .text(d => d.name) .attr('x', labelHeight * 1.2) .attr('y', (d,i) => labelHeight * i * 1.8 + labelHeight) .style('font-family', 'sans-serif') .style('font-size', labelHeight); return svg.node(); }40:T819,//Needs to be modified to graph spectralResult not ErrorVal { // code modified from https://observablehq.com/@spattana/d3-introducing // on the line graph example let svg = d3.select(DOM.svg(canvasWidth+100,canvasHeight+100)); let chart = svg.append("g").attr("transform",`translate(${50}, ${50})`); //console.log(spectralResult); //console.log(graphableFourier.centered); let results = spectralResult.map((result, index) => ({y:result, x:index})); let data = [results]; console.log(data); let xDomain = [0,spectralResult.length] let yDomain = [spectralBounds.min, spectralBounds.max]; let xScale = d3.scaleLinear().domain(xDomain).range([0, canvasWidth]).nice(); let yScale = d3.scaleLinear().domain(yDomain).range([canvasHeight, 0]).nice(); //axes let xAxis = d3.axisBottom().scale(xScale).ticks(20); let yAxis = d3.axisLeft().scale(yScale).ticks(20, ".3s"); chart.append('g').attr('transform', `translate(0, ${canvasHeight})`).call(xAxis); chart.append('g').call(yAxis) // text label for the x axis chart.append("text") .attr("transform", `translate(${canvasWidth/2},${canvasHeight + 50/1.5})`) .style("text-anchor", "middle") .text("Frequency"); // text label for the y axis chart.append("text") .attr("transform", "rotate(-90)") .attr("y", 0 - 100) .attr("x",0 - (canvasHeight / 2)) .attr("dy", "1em") .style("text-anchor", "middle") .text("Power"); // Create Title const title = svg.append("text") .attr("x", canvasWidth/2 + 100 ) .attr("y", 50/2) .style("font-size", 32) .style("text-anchor", "middle") .text("Radial Mean"); // Create lines const line = d3.line() .x(d => xScale(d.x)) .y(d => yScale(d.y)) //.curve(d3.curveCardinal); // Draw the lines. svg.append('g') .selectAll('path') .data(data) .join('path') .style("fill", "none") .attr("transform", "translate(50,50)") .style("stroke", "steelblue") .attr('d', (d) => line(d)); return svg.node(); }41:T647,//Generates sobol sequence array, computes sobol point values for 1st and 2nd dimension function sobolSeq (N,D,C,a,maxBit2) { const pointamount = N //generate sobol points array let points = new Array(N); // create 2d array since javascript is pretty weird about that for(let i = 0; i < N; i++) { points[i] = new Array(2); } // initalize for(let j = 0; j < 2; j++) { points[0][j] = 0; } //generate points[i] let dir = new Array(maxBit2 + 1); let x = new Array(pointamount); for (var i=1 ; i <= pointamount; i++) dir[i] = 1 << (32-i); // all m's = 1 // Evalulate X[0] to X[N-1], scaled by pow(2,32) x[0] = 0; for (let i = 1; i <= pointamount - 1; i++) { x[i] = x[i-1] ^ dir[C[i-1]]; points[i][0] = x[i]/Math.pow(2.0,32); // *** the actual points // ^ 0 for first dimension } //generate points[j] let m = new Array(2); m[1] = 1; let V = new Array(maxBit2 + 1); let X = new Array(N); // Compute direction numbers V[1] to V[L], scaled by pow(2,32) if (maxBit2 <= 1) { for (var i=1; i<= maxBit2 ;i++) V[i] = m[i] << (32-i); } else { for (var i=1; i <= 1 ;i++) V[i] = m[i] << (32-i); for (var i = 2; i <= maxBit2 ; i++) { V[i] = V[i-1] ^ (V[i-1] >> 1); for (var k=1; k <= 0 ; k++) V[i] ^= (((a >> (1-1-k)) & 1) * V[i-k]); } } // Evalulate X[0] to X[# of points -1], scaled by pow(2,32) X[0] = 0; for(let i = 1; i < N; i++) { X[i] = X[i-1] ^ V[C[i-1]]; points[i][1] = X[i]/Math.pow(2.0,32); } return points; }42:T98c,function radialPoisson(n, r, x, y) { var pointArray = [] var xArr = [] var yArr = [] // //This Next Section generates the initial point // var xPos = (Math.random() * x) var yPos = (Math.random() * y) xArr.push(xPos) yArr.push(yPos) let newPoint = [xPos, yPos] pointArray.push(newPoint) var activeXPoint = xArr[0] var activeYPoint = yArr[0] var impossibleCheck = 0 for (var i=1; i { // Euler's formula: // e^ix = cos(x) + i * sin(x) // we must calculate value of x and then feed it to the real value and the imaginary value of the complex number let N = listOfPoints.length // Number of points let xVal = 0 // value for x in Euler's formula let yVal = 0 let sigma = complex(0,0) // used in calculating the summation let sigmaAverage = complex(0,0) let columns = [] let row = [] if (fourier == "Disabled") return [[0,0],[0,0]] for (let i = 0; i < x; i++) // x dimension of pixelArray { for (let j = 0; j < y; j++) // y dimension of pixelArray { for (let n = 0; n < N; n++) // points { xVal = 2 * Math.PI * (((i*listOfPoints[n][0]) / x) - ((j*listOfPoints[n][1]) / y)) sigma = sigma.add(Math.cos(xVal), Math.sin(xVal)) } sigmaAverage = complex(sigma.re / (x * y), sigma.im / (x * y)) row.push(sigmaAverage) sigma = complex(0,0) sigmaAverage = complex(0,0) } columns.push(row) row = [] } // take code from scaleAndCenter to make centerListOfPoints // This must be be done to do the 1-d power spectral analysis // and to display representation (once we figure out how to handle the complex numbers) return columns 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39:{"id":"220293cee43c20b8","slug":"cap-4720-final-project-the-monte-carlo-sampler-group-presen","title":"CAP 4720 Final Project: The Monte Carlo Sampler Group Presentation FINAL ITERATION","thumbnail":"fb6b75cd554ee78d53ed0d7c17b41367f3f3407725ff48add631c753ddd82e2e","access_level":"public","create_time":"$D2020-12-10T18:59:08.209Z","update_time":"$D2020-12-11T13:26:14.274Z","view_time":null,"first_public_time":"$D2020-12-10T18:59:49.658Z","has_unpublished_edits":null,"fork":true,"stars":0,"starred":false,"owner":{"type":"team","id":"91415db2a19585e8","login":"spattana","name":"Sumant Pattanaik","avatar_url":"https://avatars-next.observableusercontent.com/5c3b1a0caf2ce230772f04126acb360531061440f39e4326260bd62e4a5e16f0","tier":"starter_2024","bio":"","followed_by_you":false,"follows_you":false},"version":1828,"publish_version":1828,"role":null,"authored":false,"authors":[{"type":"individual","id":"a51e58c27848cfd7","login":"spattana","name":"Sumant Pattanaik","avatar_url":"https://avatars-next.observableusercontent.com/5c3b1a0caf2ce230772f04126acb360531061440f39e4326260bd62e4a5e16f0","tier":null,"bio":"","followed_by_you":false,"follows_you":false}],"members":[{"type":"individual","id":"a51e58c27848cfd7","login":"spattana","name":"Sumant Pattanaik","avatar_url":"https://avatars-next.observableusercontent.com/5c3b1a0caf2ce230772f04126acb360531061440f39e4326260bd62e4a5e16f0","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":1,"collection":null,"type":"notebook","body":{"titling":"auto","title":"CAP 4720 Final Project: The Monte Carlo Sampler Group Presentation FINAL ITERATION","cells":[{"id":0,"value":"md`# CAP 4720 Final Project: The Monte Carlo Sampler Group Presentation FINAL ITERATION\nLink to the original authors' page: https://observablehq.com/d/170aad214f3df7d5`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1561,"value":"md`__Warning:__ pmj02 by its very nature is a very slow algorithm. Unlike every other implemented Monte Carlo Sampler in this document, the values of PMJ02 must be pregenerated due to how long it takes to execute. \n\nBy clicking the button below, this will pregenerate 1400 points for pmj02. Depending on your CPU and how lucky you are, this process may take 1 to 7 minutes.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1506,"value":"viewof enablePMJ02 = button()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":14,"value":"md`### Team Members\n\nTo tackle the project, we organized into 5 groups. Each group was in charge of coding up their algorithm as well as making sure their algorithm generated the outputs mentioned later in this document.\n\n__Halton Sequence__\n\nJohn Cunningham - Project Lead\n\nAlex Hillegass\n\n__Sobol Sequence__\n\nLac Quynh Nguyen\n\nAnnemarie Blanco\n\nNicholas Robelo\n\n__PMJ02__\n\nCarter Hankin - Implementation\n\nSam Rankin\n\nRobert Law - Implementation\n\n__Poisson Disk Sampling__\n\nMichael Dews\n\nSamantha Perez\n\nDavis Rollman\n\n\n__Latin Hypercubes (n-rooks)__ \n\nKolbe Benner\n\nQuintus Lamar\n\nCarlos Rodriguez\n\n\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":65,"value":"md`### Project requirements\nCode up the Halton, Sobol, pmj02, Latin Hypercube, and Poisson Disk sampling patterns and for each sampling pattern:\n- Show Sampling patterns on a 2d grid\n- Apply and display a Fourier Transformation \n- Show a power density distribution in 1D\n- Plot the error function of the number of samples\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":25,"value":"md`### Contributors to the Generalized Outputs\nTo make life easier for all the groups, the output for every sampler was standardized to be the equivalent of a javascript 2d array representing the list of points. All the outputs would accept that as their input to generate the final product.\n\n2d Grid:\n- John Cunningham \n- Michael Dews\n- Alex Hillegass\n\nFourier Transformation:\n- John Cunningham\n- Quintus Lamar\n\n1-d Spectrum Analysis:\n- Quintus Lamar\n- Davis Rollman\n- Kolbe Benner\n\nError Function:\n- Kolbe Benner\n\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1650,"value":"md`### What went right\n- Subdivision of problem\n- Output standardization\n`\n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1651,"value":"md`### What went wrong\n- Procrastination\n- Communication from Team Lead\n- Not doing what people said they were going to do\n- Figuring out how some of the algorithms are supposed to work\n- Large group\n\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":30,"value":"md`### Presentation and Paperwork\nFinal Observable notebook\n- John Cunningham - Putting everything together\n- Alex Hillegass - Definitions for the algorithms\n- Nicholas Robelo - Sobol definition\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":133,"value":"md`### What is a Monte Carlo Simulaton/Method/Algorithm?\nAccording to IBM, a Monte Carlo simulation is a method of estimating the output of an uncertain event. Basically, given an exact answer, a Monte Carlo simulation gets you an approximation of an answer and a __really__ close approximation the more points you add randomly.\n\nAlso note, that this classification of operations is very broad.\n\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1820,"value":"md`Source: https://www.ibm.com/cloud/learn/monte-carlo-simulation`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":207,"value":"md`### What are they used for?\nMonte Carlo simulations are used in many different fields of industry and research [1]. Some applications may include, but are not limited to:\n- Risk assesment\n- Detecting correlation\n- Artifical Intelligence\n- Pricing\n- Stock prices\n- Integration\n\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":112,"value":"md`### What is a Monte Carlo Sampler?\nA Monte Carlo Sampler is an application of a Monte Carlo algorithm for the purpose of integration. \n\nGiven an empty finite space and a smaller space within it, if we repeatedly added points randomly to this entire space, we can find a close approximation of what the area within or outside that space is.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":151,"value":"md`### Our sequences\n\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":163,"value":"md`#### Halton Sampler\nUses Van der Corput 1D sequence to generate values in the range [0,1).\n\nFor base 2 the numerator of the fraction is the binary decimal where the binary representation of the number is reversed.\n\nThe denominator is 2^b where b is the number of digits necessary to represent the numerator in binary.\n\nThe case below uses base 2 or binary but any prime number may be used like base 3 which uses a ternary representation.\n\nSource: http://www.pbr-book.org/3ed-2018/Sampling_and_Reconstruction/The_Halton_Sampler.html`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1678,"value":"md`${await FileAttachment(\"halton seq.PNG\").image()}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":164,"value":"md`#### Sobol Sampler`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1699,"value":"md`\nThe original implementation of the algorithm works by conducting the bit-by-bit XOR operation on a given point and a set of \"direction numbers\". The points are broken down so that the rightmost digit of the ith point(written in binary) is XOR'd with the jth component of the direction number. \n\nThe gray code implementation uses an algorithm that conducts the same operation but with binary reflected numbers instead of the calculated direction numbers. Binary reflected numbers are the same as binary numbers, but they are reordered so that each binary number only changes one by one bit as its incremented. The gray code implementation still creates all the same points just in a different order. \n\nThe benefit of using the gray code implementation over the normal implementation is that it can be done recursively and is more computationally efficient since you don't have to calculate the direction numbers. However, the normal implementation can start anywhere in the sequence.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1703,"value":"md`${await FileAttachment(\"sobol.PNG\").image()}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1795,"value":"md`Picture source: \nhttp://www.pbr-book.org/3ed-2018/Sampling_and_Reconstruction/Sobol_Sampler.html\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":166,"value":"md`#### Poisson Disk Sampler`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1693,"value":"md`Samples are picked such that they are at least r distance apart. Samples may be randomly or strategically picked. Prevents clusters because all points are relativly evenly spaced.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1695,"value":"md`${await FileAttachment(\"poisson.PNG\").image()}`\n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1706,"value":"md`Source: https://www.cct.lsu.edu/~fharhad/ganbatte/siggraph2007/CD2/content/sketches/0250.pdf\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":168,"value":"md`#### Latin Hypercube (n-rooks)\n\nSampling region is partitioned into N evenly sized regions. A random point is picked inside each region. At higher dimensions only one sample is allowed per row and column.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1686,"value":"md`${await FileAttachment(\"latin hypercube.PNG\").image()}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1688,"value":"md`Source: https://users.ece.cmu.edu/~xinli/classes/cmu_18660/Lec25.pdf\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":170,"value":"md`#### pmj02`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1712,"value":"md`Partition space and pick one sample per partition. Divide each partiton into four pieces and randomly pick another sample for each region not occupied. Continue this until desired number of samples is reached. \n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1714,"value":"md`${await FileAttachment(\"pmj.PNG\").image()}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1803,"value":"md`Source: https://graphics.pixar.com/library/ProgressiveMultiJitteredSampling/paper.pdf`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":199,"value":"md`### Fourier Transformation`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1769,"value":"md`This is the equation for the fourier transformation we have adapted to form our Fourier Transformation.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1763,"value":"md`${await FileAttachment(\"fourierEquation.png\").image()}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1771,"value":"md`Euler's equation`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1760,"value":"md`${await FileAttachment(\"eulersequation.png\").image()}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1776,"value":"md`Source:https://www.cs.bgu.ac.il/~dip111/wiki.files/DIP3E_Chapter04_Art.pdf`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1749,"value":"\nmd`\n${await FileAttachment(\"1024_45_36_Halton_FT.png\").image()}\nUncentered Fourier Transformation of the Halton sequence with 1024 points,\nbase 1 = 45\nbase 2 = 36 generated by our implementation \n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1723,"value":"md`#### Error Function`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1781,"value":"md`The error function is generated by finding the Monte Carlo Sampling of an area. We can calculate the area of a 2d shape within the total area of the finite 2d space using the following method:\n- Populate the 2d space with points\n- Count the number of points that lie within the shape\n- Divide the number of points that lie within by the total amount\n- multiply the ratio by the total area of the space to get the estimate\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":116,"value":"md`### Our work\n\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":264,"value":"md`### 2d Graph`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":294,"value":"viewof algorithmChoice = radio({\n title: 'Algorithms',\n options: [\n { label: 'Random', value: 'Random' },\n { label: 'Halton', value: 'Halton' },\n { label: 'Sobol', value: 'Sobol' },\n { label: 'Latin Hypercube', value: 'Hypercube' },\n { label: 'Poisson Disk', value: 'Poisson' },\n { label: 'pmj02', value: 'pmj02' }\n \n ],\n value: 'Halton'\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":305,"value":"md`#### Algorithm specific input`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":309,"value":"viewof toggleHaltonColor = radio({\n title: 'Toggle Color for Halton',\n options: [\n { label: 'Color', value: 'Yes' },\n { label: 'noColor', value: 'No' }\n ],\n value: 'No'\n })\n ","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":303,"value":"viewof haltonSpecific = columns({\n dim1: slider({\n min: 2,\n max: 200,\n precision: 0,\n title: \"base 1\",\n value: 199\n }),\n dim2: slider({\n min: 2,\n max: 200,\n precision: 0,\n title: \"base 2\",\n value: 200\n })\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":423,"value":"md`##### Poisson Disk Specific Input`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":356,"value":"viewof poissonSpecific = columns({\n minDistance: slider({\n min: 5,\n max: 500,\n precision: 5,\n title: \"Distance between points\",\n value: 10\n }),\n generationChoice: radio({\n title: 'Generation',\n options: [\n { label: 'Random', value: 'Random' },\n { label: 'Radial', value: 'Radial' },\n ],\n value: 'Random'\n })\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":424,"value":"md`##### Sobol specific input`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":297,"value":"viewof inputDimensions = columns({\n width: slider({\n min: 0,\n max: canvasWidth * 2,\n precision: 0,\n title: \"Max X\",\n value: canvasWidth * 2\n }),\n height: slider({\n min: 0,\n max: canvasHeight * 2,\n precision: 0,\n title: \"Max Y\",\n value: canvasHeight * 2\n })\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":300,"value":"viewof pointSpecs = columns({\n pointAmount: slider({\n min: 1,\n max: 10000,\n precision: 0,\n title: \"Number of points\",\n value: 10\n }),\n pointWidth: slider({\n min: 0.001,\n max: 6,\n precision: 5,\n title: \"Point width\",\n value: 4\n })\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":403,"value":"$3d","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":277,"value":"md`### Error Function`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":897,"value":"viewof algorithmChoice2 = radio({\n title: 'Algorithms',\n options: [\n { label: 'Random', value: 'Random' },\n { label: 'Halton', value: 'Halton' },\n { label: 'Sobol', value: 'Sobol' },\n { label: 'Latin Hypercube', value: 'Hypercube' },\n { label: 'Poisson Disk', value: 'Poisson' },\n { label: 'pmj02', value: 'pmj02' }\n \n ],\n value: 'Halton'\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":952,"value":"viewof numbaOfPoints = slider({\n min: 1,\n max: 10000,\n precision: 0,\n title: \"Number of points\",\n value: 1000\n })","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":703,"value":"$3e","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":926,"value":"viewof haltonSpecific2 = columns({\n dim1: slider({\n min: 2,\n max: 200,\n precision: 0,\n title: \"base 1\",\n value: 199\n }),\n dim2: slider({\n min: 2,\n max: 200,\n precision: 0,\n title: \"base 2\",\n value: 200\n })\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":711,"value":"$3f","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":266,"value":"md`### Fourier Transformation`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":968,"value":"viewof algorithmChoice3 = radio({\n title: 'Algorithms',\n options: [\n { label: 'Random', value: 'Random' },\n { label: 'Halton', value: 'Halton' },\n { label: 'Sobol', value: 'Sobol' },\n { label: 'Latin Hypercube', value: 'Hypercube' },\n { label: 'Poisson Disk', value: 'Poisson' },\n { label: 'pmj02', value: 'pmj02' }\n \n ],\n value: 'Halton'\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":997,"value":"viewof numbaOfPoints3 = slider({\n min: 0,\n max: 1000,\n precision: 0,\n title: \"Number of points\",\n value: 1000\n })","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1405,"value":"viewof poissonSpecific2 = slider({\n min: 5,\n max: 500,\n precision: 5,\n title: \"Distance between points\",\n value: 10\n })","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":989,"value":"viewof haltonSpecific3 = columns({\n dim1: slider({\n min: 2,\n max: 200,\n precision: 0,\n title: \"base 1\",\n value: 199\n }),\n dim2: slider({\n min: 2,\n max: 200,\n precision: 0,\n title: \"base 2\",\n value: 200\n })\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":973,"value":"viewof inputDimensions3 = columns({\n width: slider({\n min: 0,\n max: 800,\n precision: 0,\n title: \"Max X\",\n value: 800\n }),\n height: slider({\n min: 0,\n max: 800,\n precision: 0,\n title: \"Max Y\",\n value: 800\n })\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":556,"value":"viewof fourier = radio({\n title: 'Fourier transformation',\n options: [\n { label: 'Enabled', value: \"Enabled\" },\n { label: 'Disabled', value: 'Disabled' },\n ],\n description: \"WARNING, MAKE SURE TO USE SMALL AMOUNT OF POINTS AND/OR DIMENSIONS (If Observable gives you a pop-up, just dismiss it)\",\n value: 'Disabled'\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":564,"value":"viewof fourierPixelSize = slider({\n min: 0.001,\n max: 10,\n precision: 3,\n title: \"Pixel Size\",\n value: 2\n })","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":565,"value":"viewof fourierGamma = slider({\n min: 1,\n max: 10000,\n precision: 0,\n title: \"Gamma\",\n value: 1000\n })","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":561,"value":"viewof fourierView = radio({\n title: 'Center Origin',\n options: [\n { label: 'Enabled', value: \"Enabled\" },\n { label: 'Disabled', value: 'Disabled' },\n ],\n description: \"Origin at center translates the graph so that the origin is not in a corner, but is rather at the center of the graphic.\",\n value: 'Enabled'\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":567,"value":"{\n const fourierCanvas = DOM.canvas(inputDimensions3.width, inputDimensions3.height)\n const gl = regl({canvas:fourierCanvas});\n gl.clear({color: [0, 0, 0, .5]})\n var drawPoint\n var targetList\n \n if(fourier == \"Enabled\")\n {\n if (fourierView == \"Enabled\")\n drawPoint = gl(drawFourierPoints(graphableFourier.centered, graphableFourier.colors, fourierPixelSize, inputDimensions3.width/2, inputDimensions3.height/2));\n \n else \n drawPoint = gl(drawFourierPoints(graphableFourier.points, graphableFourier.colors, fourierPixelSize, inputDimensions3.width/2, inputDimensions3.height/2));\n \n \n drawPoint();\n }\n \n return fourierCanvas;\n}\n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":273,"value":"md`### 1-d Spectral Analysis`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":610,"value":"$40","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":381,"value":"md`## Algorithms`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":409,"value":"md`#### Random points`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":730,"value":"function randomPoints(n, x, y) {\n \n var pointArray = [];\n var colorArray = [];\n for (var i = 0; i < n; i++) {\n let newPoint = [\n Math.random() * x,\n Math.random() * y\n ];\n let newColor = [0, Math.random(), 0];\n\n pointArray.push(newPoint);\n colorArray.push(newColor);\n }\n \n return { pointList: pointArray, colors: colorArray };\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":411,"value":"md`#### Halton Sequence`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1814,"value":"md`adapted from wikipedia: https://en.wikipedia.org/wiki/Halton_sequence`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":805,"value":"function haltonArray(n, primes, x ,y) {\n let out = [];\n\n const haltonPoints = haltonSequence(n, primes, x, y)\n\n return out\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":809,"value":"function haltonSequence(length, primes, x, y){\n // You must supply the prime numbers to use in this simulation\n // The number that you supply will determine the number of sequences calculated\n // Two primes gives us the 2D array with an X and a Y coordinate\n var sequence = [];\n var dimensions = [x, y]\n var target = 0;\n var output = []\n var p = 0;\n var somevar = 0;\n \n for (var j = 0; j < length; j++)\n {\n output.push([])\n }\n \n for(var i = 0; i < primes.length; i++){\n p = primes[i];\n sequence[i] = [];\n for(var j = 0; j < length; j++){\n output[j][i] = haltonNumber(j+1, p) * dimensions[i];\n }\n }\n return output\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":811,"value":"function haltonNumber(i, b) {\n // Courtesy of Wikipedia pseudocode\n // https://en.wikipedia.org/wiki/Halton_sequence\n var f = 1;\n var r = 0;\n while (i > 0) {\n f = f / b;\n r = r + f * (i % b);\n i = Math.floor(i / b);\n }\n return r;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":816,"value":"function haltonColors(n, haltonArray) {\n let colors = [];\n for (let i = 0; i < n; i++) {\n if (toggleHaltonColor == 'Yes') {\n if (i % 2) colors.push([1, 0, 0]);\n else colors.push([0, 0, 1]);\n } else {\n colors.push([0, 0, 0]);\n }\n }\n\n return colors;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":813,"value":"function haltonPointsList(n, primes, x, y) {\n var output = haltonSequence(n, primes, x, y)\n return {pointList: output, colors: haltonColors(n, output)}\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":386,"value":"primes = [haltonSpecific.dim1, haltonSpecific.dim2]\n// How we will divide x,y,z .... nth dimension","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":429,"value":"md`### Sobol Algorithm`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1811,"value":"md`Adapted from sobol.cc: https://web.maths.unsw.edu.au/~fkuo/sobol/`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":435,"value":"SobolArray = (amount,x, y) => {\n //Runs the Sobol Sequence\n let array = sobolSeq(amount,2,C(amount),a,maxBit(amount));\n //Fixes negative points issue\n array = adjustPoints(array)\n //Scales points to fit in the graph\n array = scaleListOfPoints(array,x, y*2)\n return array;\n}\n ","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":437,"value":"//Applies color to points\nsobolColors = {\n //just black points \nlet colors = []\nfor(let i = 0; i < pointSpecs.pointAmount; i++)\n {\n colors.push([0,0,0])\n }\nreturn colors\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":439,"value":"$41","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":486,"value":"maxBit = (pointSpecs) => {\n return Math.ceil(Math.log2(pointSpecs))\n} // get max # of bits needed","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":490,"value":"//\nC = (amount) => { // based on the sobol.cc sobol_points function in https://web.maths.unsw.edu.au/~fkuo/sobol/\n let arr = new Array(amount);\n arr[0] = 1;\n // C[i] = index from the right of the first zero bit of i\n for(let i = 1; i <= amount - 1; i++) {\n arr[i] = 1;\n let value = i;\n //Populates arr with \"1\" in every even index\n //Populates every odd index by incrementing until value/2 is even\n while( value & 1) {\n value >>= 1;\n arr[i]++;\n }\n }\n return arr;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":495,"value":"a = 0;","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":472,"value":"function adjustPoints(listOfPoints) {\n //moves negative points to Quadrent 1\n let output = []\n let target = []\n \n for(let i = 0; i < listOfPoints.length; i++)\n {\n if(listOfPoints[i][0] < 0)\n { \n target[0] = listOfPoints[i][0] + 1\n target[1] = listOfPoints[i][1] * -1\n }\n \n else\n {\n target[0] = listOfPoints[i][0]\n target[1] = listOfPoints[i][1]\n }\n \n output.push(target)\n target = []\n }\n \n return output\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":477,"value":"test = sobolSeq(pointSpecs.pointAmount,2,C(pointSpecs.pointAmount),a,maxBit(pointSpecs.pointAmount))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":470,"value":"output = adjustPoints(test)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":591,"value":"md`### Latin HyperCube`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":595,"value":"// knuth shuffle\nfunction shuffleArray(array) {\n for (var i = array.length - 1; i > 0; i--) {\n var j = Math.floor(Math.random() * array.length);\n\n var temp = array[i];\n array[i] = array[j];\n array[j] = temp;\n }\n return array;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":596,"value":"function lhcPoint(n, x1, y1) {\n var xValues = [];\n var yValues = [];\n\n const xInterval = x1 / n;\n const yInterval = y1 / n;\n\n/* for (var x = 0.0; x < n; x++)\n xValues.push( (Math.random() * xInterval) + (x * xInterval) );\n for (var y = 0.0; y < n; y++)\n yValues.push( (Math.random() * yInterval) + (y * yInterval) );\n*/\n \n for (var i = 0.0; i < n; i++) {\n xValues.push(Math.random() * xInterval + i * xInterval);\n yValues.push(Math.random() * yInterval + i * yInterval);\n }\n xValues = shuffleArray(xValues);\n yValues = shuffleArray(yValues);\n\n var color = [];\n var points = [];\n for (var i = 0; i < n; i++) {\n points.push([xValues[i], yValues[i]]);\n color.push([1, 0, 1]);\n }\n\n return { pointList: points, colors: color};\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1462,"value":"md`### PMJ02`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1469,"value":"md`Adapted from: \nhttps://graphics.pixar.com/library/ProgressiveMultiJitteredSampling/pmj_suppl.pdf`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1510,"value":"enablePMJ02BOOL = {\n enablePMJ02\n return !this;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1472,"value":"samples = [];","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1475,"value":"function initSamples()\n{\n samples.length = 0;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1476,"value":"occupiedStrata = [];","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1478,"value":"function initOccupiedStrata(N)\n{\n var NN = 2*N;\n // clear array if it already exists\n occupiedStrata.length = 0;\n \n for (var x = 0; x <= Math.log2(NN); x++)\n {\n var row = [NN];\n for (var y = 0; y <= NN-1; y++)\n {\n row[y] = false;\n }\n occupiedStrata[x] = row;\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1484,"value":"function markOccupiedStrata(N)//this function isn't used in the original pseudocode. It's intended to go mark all the old strata so that we don't go back over them, but we're already doing this as part of the generateSamplePoint function.\n{\n var NN = 2 * N;\n // loop over samples and mark occupied strata\n for(var s = 0; s <= 183-1; s++) {\n markOccupiedStrata1(samples[s], NN);\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1485,"value":"function markOccupiedStrata1(pt, NN)\n{\n var shape = 0;\n var xdivs = NN;\n var ydivs = 1;\n \n do\n {\n var xstratum = Math.floor(xdivs * pt[0]);\n var ystratum = Math.floor(ydivs * pt[1]);\n \n occupiedStrata[shape][ystratum * xdivs + xstratum] = true;\n \n shape = shape + 1;\n xdivs = Math.floor(xdivs / 2);\n ydivs = ydivs * 2;\n \n console.log(\"markOccupiedStrata1 \" + xdivs); // TODO debug\n\n } while (xdivs != 0);\n}\n ","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1489,"value":"\nfunction generateSamplePoint(i, j, xhalf, yhalf, n, N)\n{\n var NN = 2 * N;\n // generate x and y until sample is accepted as a (0,2) sample\n var pt = [2];\n pt.length = 2;\n do\n {\n var x = (i + 0.5 * (xhalf + Math.random())) / n;\n var y = (j + 0.5 * (yhalf + Math.random())) / n;\n //pt = new Point(x, y);\n pt[0] = x;\n pt[1] = y;\n console.log(\"generateSamplePoint \" + pt + \", \" + NN); // TODO debug\n } while (isOccupied(pt, NN));\n\n // mark strata that this new sample occupies\n markOccupiedStrata1(pt, NN);\n\n // assign a new sample point\n samples.push(pt);\n}\n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1491,"value":"\nfunction isOccupied(pt, NN)//according to debugs this is the current error source\n{\n var shape = 0;\n var xdivs = NN;\n var ydivs = 1;\n \n do\n {\n var xstratum = Math.floor(xdivs * pt[0]);\n var ystratum = Math.floor(ydivs * pt[1]);\n\n if(occupiedStrata[shape][ystratum * xdivs + xstratum])\n {\n return true; // this is because the stratum is already occupied\n }\n\n shape = shape + 1;\n xdivs = Math.floor(xdivs / 2);\n ydivs = ydivs * 2;\n \n console.log(\"isOccupied \" + xdivs); // TODO debug\n\n } while (xdivs != 0);\n \n return false; // it is ok to use this space as sample pt is not in any occupied stratum\n}\n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1493,"value":"function pmj(N, r)\n{\n const i = 0;\n const j = 0;\n const xhalf = 0;\n const yhalf = 0;\n const n = 1;\n \n if (r > 1400){\n r = 1400;\n }\n \n initSamples();\n initOccupiedStrata(N);\n \n for (var z = 0; z < r; z++)\n {\n generateSamplePoint(i, j, xhalf, yhalf, n, N);\n //markOccupiedStrata(N);\n }\n\n \n return samples;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1499,"value":"pmj02TotalListOfPoints = {\n var N = 4096;\n var r = 1416;\n if (!enablePMJ02BOOL)\n pmj(N, r);\n\n return samples;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1528,"value":"pmj02Output = (amount, x, y) => {\n if (amount > 4096)\n amount = 4096\n \n var outputArray = pmj02TotalListOfPoints.slice(0, amount)\n var colorsArray = []\n \n for (let i = 0; i < amount; i++)\n colorsArray.push([230/256,177/256,0/256])\n \n return {pointList: scaleListOfPoints(outputArray, x, y), colors:colorsArray} \n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1211,"value":"md`### Poisson Disk Sampling`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1789,"value":"md` Adapted from: https://observablehq.com/@nextlevelshit/fast-poisson-disk-sampling`","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1213,"value":"function poissonColors(poissonArray) {\n let colors = [];\n for (let i = 0; i < poissonArray.length; i++) {\n colors.push(0, Math.random(), 0);\n }\n return { colors: colors };\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1215,"value":"$42","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1217,"value":"function randomPoisson(n, r, x, y) {\n var pointArray = []\n\n\n var xPos = (Math.random() * x)\n var yPos = (Math.random() * y)\n let newPoint = [xPos, yPos]\n \n pointArray.push(newPoint)\n\n var impossibleCheck = 0\n \n \n \n for (var i=1; i ({ \n // How WebGL will process verticies \n vert: `\n precision mediump float;\n attribute vec2 position;\n\n void main() {\n vec2 position2 = position;\n vec4 targetPosition = vec4(position2, 0, 1.0);\n gl_Position = targetPosition;\n }\n `,\n\n // How WebGL will handle shading\n frag: `\n precision mediump float;\n\n void main () {\n gl_FragColor = vec4(0, 0, 0, .66);\n }\n `,\n\n // Variables associated with the vectors\n attributes: {\n position: normals1,\n },\n\n // contains information shared between the shader and openGL. Global scope.\n uniforms:{\n\n },\n\n // This is a list of all the triangles required to make the shape\n elements: cells1,\n\n\n // determines whether to render shape using triangles or points\n primitive: \"triangles\"\n\n })\n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":445,"value":"xAxisList = generateXAxis(7)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":449,"value":"yAxisList = generateYAxis(7)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":451,"value":"generateXAxis = (xDimension) => \n{\n var center = [0, 0]\n var xList = []\n var count = 1\n var xOffset = .25\n var targetOffset = 0\n \n for (var i = 0; i < xDimension; i++)\n {\n \n xList.push(({\n positions: [[1, -.001 + targetOffset], \n [1, .001 + targetOffset], \n [-1, .001 + targetOffset], \n [-1, -.001 + targetOffset]],\n cells: [[0,1,2], [2,3,0]],\n normals: [[0, 0, 1],[0, 0, 1],[0, 0, 1],]\n })\n )\n \n if(i == 0 || !(i % 2))\n {\n targetOffset *= -1\n targetOffset += xOffset\n }\n \n else\n targetOffset *= -1\n \n }\n \n return xList\n \n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":453,"value":"generateYAxis = (yDimension) => \n{\n var center = [0, 0]\n var xList = []\n var count = 1\n var xOffset = .25\n var targetOffset = 0\n \n for (var i = 0; i < yDimension; i++)\n {\n \n xList.push(({\n positions: [[.001 + targetOffset, -1], \n [.001 + targetOffset, 1], \n [-.001 + targetOffset, 1], \n [-.001 + targetOffset, -1]],\n cells: [[0,1,2], [2,3,0]],\n normals: [[0, 0, 1],[0, 0, 1],[0, 0, 1],]\n })\n ) \n if(i == 0 || !(i % 2))\n {\n targetOffset *= -1\n targetOffset += xOffset\n }\n \n else\n targetOffset *= -1\n \n }\n \n return xList\n \n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":455,"value":"yAxisObject = ({\n positions: [[.001, -1], [.001, 1], [-.001, 1], [-.0005, -1]],\n cells: [[0,1,2], [2,3,0]],\n normals: [[0, 0, 1],[0, 0, 1],[0, 0, 1],]\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":457,"value":"xAxisObject = ({\n positions: [[1, -.001], [1, .001], [-1, .001], [-1, -.001]],\n cells: [[0,1,2], [2,3,0]],\n normals: [[0, 0, 1],[0, 0, 1],[0, 0, 1],]\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":467,"value":"drawPoints = (points1, colors1, pointWidth1) => ({\n vert: `\n precision highp float;\n attribute vec2 position;\n attribute vec3 color;\n varying vec3 fragColor;\n uniform float pointWidth, width, height;\n\n vec2 normalizeCoords(vec2 position){\n float x = position[0];\n float y = position[1];\n\n return vec2(((x/width) - 1.), (((y/height) - 1.)));\n }\n\n void main(){\n gl_PointSize = pointWidth;\n fragColor = color;\n gl_Position = vec4(normalizeCoords(position), 0.0, 1.0);\n }\n `,\n frag: `\n\t precision highp float;\n\t\tvarying vec3 fragColor;\n\n\t\tvoid main() {\n\t\t\tgl_FragColor = vec4(fragColor, 1);\n\t\t}\n\t\t`,\n \n attributes:{\n position: points1,\n color: colors1\n },\n \n uniforms:{\n pointWidth: pointWidth1,\n width: canvasWidth,\n height: canvasHeight,\n },\n \n count: points1.length,\n \n \n primitive: 'points',\n});","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":713,"value":"md`### Error Dependencies`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":716,"value":"$43","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":719,"value":"function findError(n, points, x, y){\n var trueShapeArea = x * y *.5 *.5\n const trueGraphArea = x * y \n \n var pointsInside = 0\n \n for(var i = 0;i < n; i++){\n var point = points[i]\n // check if point is inside shape\n if(point[0]/x - 1 < .5 && point[0]/x - 1 > -.5){\n if(point[1]/y - 1 < .5 && point[1]/y - 1 > -.5){\n pointsInside += 1\n }\n }\n }\n const predictedAreaofShape = pointsInside/n*trueGraphArea\n const percError = Math.abs((predictedAreaofShape - trueShapeArea)/trueShapeArea * 100)\n return percError\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":721,"value":"testErrorShape = (shape) => ({\nvert: `\n precision mediump float;\n attribute vec2 position;\n\n void main() {\n vec2 position2 = position;\n vec4 targetPosition = vec4(position2, 0, 1.0);\n gl_Position = targetPosition;\n }\n `,\n\n frag: `\n precision mediump float;\n\n void main () {\n gl_FragColor = vec4(0, 0, 0, .7);\n }\n `,\n\n // Variables associated with the vectors\n attributes: {\n position: shape.positions\n },\n\n elements: shape.cells,\n primitive: \"triangles\"\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":722,"value":"shape = ({positions: [[-.5,-.5],[-.5,.5],[.5,-.5],[.5,.5]],\n cells: [[0,1,2], [1,3,2]]})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":725,"value":"shape2 = ({positions: [[-.5,-.5],[-.5,.5],[.5,-.5]],\n cells: [[0,1,2]]})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":538,"value":"md`### Fourier Dependencies`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":546,"value":"graphableFourier = convertFourierResultToPoints(FourierResult, inputDimensions3.width, inputDimensions3.height)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":577,"value":"drawFourierPoints = (points1, colors1, pointSize, x, y) => ({\n vert: `\n precision highp float;\n attribute vec2 position;\n attribute vec3 color;\n varying vec3 fragColor;\n uniform float pointWidth, width, height;\n\n vec2 normalizeCoords(vec2 position){\n float x = position[0];\n float y = position[1];\n\n return vec2(((x/(width)) - 1.), (((y/(height)) - 1.)));\n }\n\n void main(){\n gl_PointSize = pointWidth;\n fragColor = color;\n gl_Position = vec4(normalizeCoords(position), 0.0, 1.0);\n }\n `,\n frag: `\n\t precision highp float;\n\t\tvarying vec3 fragColor;\n uniform float gamma;\n\n\t\tvoid main() {\n \n\t\t\tgl_FragColor = vec4(fragColor.x*gamma, fragColor.y*gamma, fragColor.z*gamma, 1);\n\t\t}\n\t\t`,\n \n attributes:{\n position: points1,\n color: colors1\n },\n \n uniforms:{\n pointWidth: pointSize,\n width: x,\n height: y,\n gamma: fourierGamma,\n },\n \n count: points1.length,\n \n \n primitive: 'points',\n});","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":547,"value":"$44","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":550,"value":"FourierResult = {\n const x = inputDimensions3.width\n const y = inputDimensions3.height\n \n if (fourier == \"Disabled\")\n return [0]\n \n if (algorithmChoice3 == \"Halton\")\n return fourierTransform(haltonPointsList(numbaOfPoints3, [haltonSpecific3.dim1, haltonSpecific3.dim2], x, y).pointList, x, y)\n \n else if (algorithmChoice3 == \"Sobol\")\n return fourierTransform(SobolArray(numbaOfPoints3, x,y), x, y)\n \n else if (algorithmChoice3 == \"Random\")\n return fourierTransform(randomPoints(numbaOfPoints3, x,y).pointList, x, y)\n \n else if (algorithmChoice3 == \"Hypercube\")\n return fourierTransform(lhcPoint(numbaOfPoints3, x,y).pointList, x, y)\n \n else if (algorithmChoice3 == \"Poisson\")\n return fourierTransform(randomPoisson(numbaOfPoints3, poissonSpecific2, x,y).pointList, x, y)\n \n else if (algorithmChoice3 == \"pmj02\")\n return fourierTransform(pmj02Output(numbaOfPoints3, x, y).pointList, x, y)\n}\n\n// DANGER- CPU INTENSIVE","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":552,"value":"convertFourierResultToPoints = (complexArray, x, y) => {\n let coordinates = [] \n let color = []\n let innerProduct = 0\n \n for (let i = 0; i < complexArray.length; i++) // x\n { \n for (let j = 0; j < complexArray[0].length; j++) // y\n {\n coordinates.push([i, j])\n innerProduct = Math.log((1 + Math.sqrt(Math.pow(complexArray[i][j].re, 2) + Math.pow(complexArray[i][j].im, 2))))\n color.push([innerProduct, innerProduct, innerProduct])\n innerProduct = 0\n }\n }\n \n return {points: coordinates, colors: color, centered: centerFourierOrigin(coordinates, x, y)}\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":553,"value":"centerFourierOrigin = (fourierCoordinates, x, y) => {\n// The convertFourierResultToPoints does not center the origin, but rather the origin exists\n// on the corners. To fix this issue, we must split the graph into 4 parts and translate the parts to\n let newList = []\n let coordinate = []\n let testCoordinate = []\n \n for (let i = 0; i < fourierCoordinates.length; i++)\n {\n testCoordinate = [...fourierCoordinates[i]]\n \n if (testCoordinate[0] < Math.floor(x/2))\n {\n coordinate.push(Math.floor(x/2) + testCoordinate[0])\n }\n else\n {\n coordinate.push(testCoordinate[0] - Math.floor(x/2))\n }\n \n if (testCoordinate[1] < Math.floor(y/2))\n {\n coordinate.push(Math.floor(y/2) + testCoordinate[1])\n }\n else {\n coordinate.push(testCoordinate[1]- Math.floor(y/2))\n }\n \n newList.push(coordinate)\n coordinate = []\n }\n \n return newList\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":619,"value":"md`### 1-d Spectral Analysis Dependencies`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":673,"value":"spectralBounds = {\n let max = 0\n let min = 0\n \n for (let i = 0; i < spectralResult.length; i++)\n {\n if (spectralResult[i] >= max)\n max = spectralResult[i]\n else\n min = spectralResult[i]\n }\n \n return {max: max * 1.1, min: min * .8}\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":616,"value":"spectralResult = spectralAnalysis(graphableFourier.centered, graphableFourier.colors, inputDimensions3.width, inputDimensions3.height)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":621,"value":"spectralAnalysis = (centered, colors, width, height) => {\n let radius = 2\n let dist = 0\n let sum = 0\n let pointCount = 0\n let resArray = []\n let radiusPitch = 2\n let max = 0\n \n \n while (radius < Math.min(width / 2, height / 2))\n {\n pointCount = 0\n sum = 0\n for (let i = 0; i < width * height; i++)\n {\n \n dist = Math.pow((centered[i][0] - width / 2), 2) + Math.pow((centered[i][1] - height / 2), 2)\n if (dist <= Math.pow(radius, 2) && dist >= Math.pow(radius - radiusPitch, 2))\n {\n pointCount++\n sum += colors[i][0]\n \n }\n }\n \n resArray.push(sum / pointCount)\n if (sum / pointCount > max)\n {\n max = sum/pointCount \n }\n \n radius += radiusPitch;\n }\n \n for (let i = 0; i < resArray.length; i++)\n {\n resArray[i] = resArray[i] / max\n }\n\n\n return resArray\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":367,"value":"md`### Loose variables and utility functions`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":628,"value":"scaleAndCenter = (listOfPoints, x, y) => {\n // given a normalized list of points...\n // this function shifts the origin from being in the bottom left to the center of the graph\n var target = scaleListOfPoints(listOfPoints, x, y)\n var output = []\n for (let i = 0; i < listOfPoints.length; i++)\n {\n var point = []\n point[0] = target[i][0] - x/2\n point[1] = target[i][1] - y/2\n output.push(point)\n point = []\n }\n \n \n return output\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":468,"value":"normalizeListOfPoints = (listOfPoints) => {\n var output = []\n for (let i = 0; i < listOfPoints.length; i++)\n {\n var point = []\n point[0] = listOfPoints[i][0] / canvasWidth\n point[1] = listOfPoints[i][1] / canvasHeight\n output.push(point)\n point = []\n }\n \n return output\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":500,"value":"scaleListOfPoints = (listOfPoints, x, y) => {\n // given a normalized list of points\n // scale the points to fit within a certain 2d boundary\n var output = []\n for (let i = 0; i < listOfPoints.length; i++)\n {\n var point = []\n point[0] = listOfPoints[i][0] * x\n point[1] = listOfPoints[i][1] * y\n output.push(point)\n point = []\n }\n \n return output\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":361,"value":"canvasWidth = 750","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":364,"value":"canvasHeight = 900","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":365,"value":"pointWidth = pointSpecs.pointWidth","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":236,"value":"md`### Imports`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":250,"value":"import { columns } from \"@bcardiff/observable-columns\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":246,"value":"import { radio, slider, color, button } from \"@jashkenas/inputs\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":244,"value":"regl = require(\"regl\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":242,"value":"createCamera = require('https://bundle.run/regl-camera@2.1.1')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":241,"value":"glMatrix = require('https://bundle.run/gl-matrix@3.3.0')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":239,"value":"d3 = require(\"d3\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":570,"value":"complex = require(\"complex.js\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":140,"value":"md`### References`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W45","stdlib":"1"}} 34:null