2e:null 2f:["$","title",null,{"children":"Infrared Sensor Transform Utility | Nikolai Nekrutenko | Observable"}] 34:T48a,Plot.plot({ // title: "IR Sensor Projection onto Hotplate", x: { label: "← X [m] →", labelAnchor: "center" }, y: { label: "← Y [m] →", labelAnchor: "center" }, grid: true, inset: 10, aspectRatio: 1, width: 640 * 1.5, color: { legend: true }, // height: 480 * 1.5, aspectRatio: 1, marks: [ Plot.frame(), Plot.dot(plot_ir_center, { x: "x", y: "y", stroke: "steelblue", strokeWidth: 1.5, r: 1.5 }), // Dots Plot.dot(plot_tc_center, { x: "x", y: "y", stroke: "#d1615d", strokeWidth: 2 }), ...ir_rows_plot.map((line) => Plot.line([line.p1, line.p2], { stroke: "steelblue", strokeWidth: 1.5 }) ), ...ir_cols_plot.map((line) => Plot.line([line.p1, line.p2], { stroke: "steelblue", strokeWidth: 1.5 }) ), ...tc_rows_plot.map((line) => Plot.line([line.p1, line.p2], { stroke: "#d1615d", strokeWidth: 1.5 }) ), ...tc_cols_plot.map((line) => Plot.line([line.p1, line.p2], { stroke: "#d1615d", strokeWidth: 1.5 }) ) ] })35:T892,As the sensor is not directly overhead of the target surface setup, an image transform must be computed. Every pixel on the infrared (IR) sensor must be mapped onto the hotplate coordinate system in order to correlate the pixel reading to the temperature of the hotplate via the thermocouple readings. The IR sensor’s field of view (FOV) plane is not parallel to the hot plate due to its mounting location at a Y and Z offset along with a tilt angle along the X-axis relative to the center of the hot plate. To take this into account, the projection of the boundaries for every pixel onto the thermocouple (TC) boundaries is mapped, and only the pixels that have their boundaries fully contained by the target surface are analyzed. In Fig. 1 and Fig. 2, the global reference frame is at the center of the Hot Plate. θ represents the tilt angle, or rotation about the X-axis. For θ at 0 degrees, the sensor faces in the -Z direction, and when θ is at 90 degrees the sensor is looking ahead in the +Y direction. φₓ and φᵧ represents the FOV of the IR Sensor in the X and Y axes, respectively. After discussing the underlying principles of such a transform, we made the assumption that when directly normal to the surface that it is mapping, the lens of the sensor ensures that every pixel sees an identical area. This means that each individual pixel does not have an identical field of view as its neighbors. If the camera is not normal to the surface, but is tilted relative to normal as is our case, the projection of camera pixels onto the target surface plane form an isosceles trapezoid with angle ${tex`\beta`} relative to the plane of the base. To support this point, looking at Fig. 1 and Fig. 2, we see that the dotted line on the top, or the upper pixels of the thermopile array are observing the object from a greater distance then the bottom pixels of the dotted line on the bottom. Since φₓ and φᵧ are constant, the greater the overall distance, the greater the area observed in X and Y. Simply put, the upper pixels are observing a larger area then the lower ones, thus the isosceles trapezoid projection shape. The trigonometric mechanism is outlined below. 36:T518,### Variable Derivations The length of the smallest base of the projection is calculated: ${tex.block` \begin{aligned} {l}_0 = \frac{2z \tan(\phi_x / 2)}{\cos(\theta - \phi_y / 2)} \end{aligned} `} The starting y-coordinate of the transform is calculated as follows: ${tex.block` \begin{aligned} y_0 = y + z \tan(\theta - \phi_y / 2) \end{aligned} `} The scaling factor, or factor by which each subsequent spacing is calculated by taking a ratio of the widths of the bases of the projection. Note the $1/n_y$ in the exponent: ${tex.block` \begin{aligned} s_{factor} = \left(\frac{1 / \cos(\theta + \phi_y / 2)}{1 / \cos(\theta - \phi_y / 2)}\right)^{1 / n_y} = \left(\frac{\cos(\theta - \phi_y / 2)}{\cos(\theta + \phi_y / 2)}\right)^{1 / n_y} \end{aligned} `} The angle of the isoceles trapezoid is calculated as such: ${tex.block` \begin{aligned} \beta = \arctan\left(\frac{\tan(\phi_x / 2) \left(\frac{1}{\cos(\phi_y / 2 + \theta)} - \frac{1}{\cos(\phi_y / 2 - \theta)}\right)}{\tan(\theta + \phi_y / 2) - \tan(\theta - \phi_y / 2)}\right) \end{aligned} `} The initial spacing (from the bottom most row to the one above) in the y-axis is calculated as such: ${tex.block` \begin{aligned} s_{init} = l_0 \cdot \frac{s_{factor} - 1}{2 \tan(\beta)} \end{aligned} `}37:Td8a,### Creating Arrays with the Transformed Coordinates for Every Pixel _Note:_ Coordinate arrays of x and y coordinates are created for the pixel boundaries, the pixel centers are mapped with another function First, the x and y arrays are initialized: > _In code_: ``` # y coordinate array initialized with n_y + 1 rows of 0's y_array = np.zeros(n_y + 1) # x coordinate array initialized with n_y + 1 rows of 0's by n_x + 1 columns of 0's x_array = np.zeros((n_y + 1, n_x + 1)) # array of initial x spacing coordinates, n_x + 1 pixels evenly spaced between the base length init_x_array = np.linspace(-l_0 / 2, l_0 / 2, num = n_x + 1) # setting the x_array's first row to the initial x spacing coordinates x_array[0] = init_x_array + x ``` > _In LaTeX_: ${tex.block` \begin{aligned} y_{array} = \begin{bmatrix} 0 \\ \vdots \\ 0 \end{bmatrix} \end{aligned} `} ${tex.block` \begin{aligned} x_{arr_{init}} = \begin{bmatrix} -l_0/2 & \dots & l_0/2 \end{bmatrix} \end{aligned} `} ${tex.block` \begin{aligned} x_{array} = \begin{bmatrix} x & \dots & x \\ \vdots & \ddots & \vdots \\ -l_0/2 + x & \dots & l_0/2 + x \end{bmatrix} \end{aligned} `} Since there is only a tilt about the x-axis, y-values are constant for each row of pixels. Thus, `y_array` is a 1D array and `x_array` is a 2D array. Then, a for loop is used to populate these arrays with x and y locations of pixels based on the variables defined above: > _In code_: ``` # loop over all rows except for the first one, populating the 0's of the arrays with values for row_index in range(n_y): # the next of row (row above) of the y array is equivalent to the previous # + the initial spacing multiplied by the scaling factor # to the power of the row index, as the spacing linearly increases y_array[row_index + 1] = y_array[row_index] + spacing_init * scaling_factor ** row_index # the next of row (row above) of the x array is equivalent to the previous # + the initial spacing x array multiplied by the scaling factor # to the power of the row index + 1, as the spacing linearly increases # then the x coordinate of the sensor offset is added x_array[row_index + 1] = init_x_array * scaling_factor ** (row_index + 1) + x # shift all values in the y coordinate array by the y coordinate of the bottom most row y_array += y_0 ``` > _In LaTeX_: ${tex.block` \begin{aligned} y_{arr}[\text{row}_{index} + 1] = y_{arr}[\text{row}_{index}] + (s_{init} \cdot s_{factor})^{\text{row}_{index}} \end{aligned} `} ${tex.block` \begin{aligned} x_{arr}[\text{row}_{index} + 1] = (x_{arr_{init}} \cdot s_{factor})^{\text{row}_{index} + 1} + x \end{aligned} `} > The for loop equations above result in the following final arrays below: ${tex.block` \begin{aligned} y_{array} = \begin{bmatrix} y_f \\ \vdots \\ y_0 \end{bmatrix} \end{aligned} `} > _Note:_ ${tex`y_f`} is the y coordinate of the top row of coordinates, this is not written out as an equation as there is recursion occurring unlike for ${tex`x_{array}`}. ${tex.block` \begin{aligned} x_{array} = \begin{bmatrix} (x_{arr_{init}}[0] \cdot s_{factor})^{n_y + 1} + x & \dots & (x_{arr_{init}}[-1] \cdot s_{factor})^{n_y + 1} + x \\ \vdots & \ddots & \vdots \\ -l_0/2 + x & \dots & l_0/2 + x \end{bmatrix} \end{aligned} `}38:T435,function tcBoundariesProjArr(TCDimensions, TCResolution, offset = [0, 0]) { // pulling data from the input lists to the arrays const nX = TCResolution[0]; const nY = TCResolution[1]; const widthX = TCDimensions[0]; const heightY = TCDimensions[1]; const offsetX = offset[0]; const offsetY = offset[1]; // Create X and Y arrays using linspace equivalent const xArray = Array.from( { length: nX + 1 }, (_, i) => -widthX / 2 + (widthX / nX) * i + offsetX ); const yArray = Array.from( { length: nY + 1 }, (_, i) => -heightY / 2 + (heightY / nY) * i + offsetY ); // Create meshgrid const meshgridX = []; const meshgridY = []; for (let i = 0; i <= nY; i++) { const rowX = []; const rowY = []; for (let j = 0; j <= nX; j++) { rowX.push(xArray[j]); rowY.push(yArray[i]); } meshgridX.push(rowX); meshgridY.push(rowY); } // Stack the meshgrid arrays along a new axis const stackedArray = meshgridX.map((rowX, i) => rowX.map((x, j) => [x, meshgridY[i][j]]) ); return stackedArray; }39:T981,function boundariesProjArr(posList, fovList, tilt, resolution) { // pulling data from the input lists to the arrays const xIR = posList[0]; const yIR = posList[1]; const zIR = posList[2]; const xFov = (Math.PI / 180) * fovList[0]; // Convert degrees to radians const yFov = (Math.PI / 180) * fovList[1]; // Convert degrees to radians const tiltAngle = (Math.PI / 180) * tilt; // Convert degrees to radians const nX = resolution[0]; const nY = resolution[1]; // bottom X "width" if (tiltAngle === 0) { const xOverheadDim = Math.tan(xFov / 2) * zIR * 2; const yOverheadDim = Math.tan(yFov / 2) * zIR * 2; const overheadDimensions = [xOverheadDim, yOverheadDim]; // need to apply a constant offset to an array return tcBoundariesProjArr(overheadDimensions, resolution, [xIR, yIR]); // Assuming tcBoundariesProjArr is defined elsewhere } else { var width1 = 2 * (zIR / Math.cos(tiltAngle - yFov / 2)) * Math.tan(xFov / 2); } // bottom Y "height" const YBound1 = yIR + zIR * Math.tan(tiltAngle - yFov / 2); // total scaling factor const totalScale = Math.pow( 1 / Math.cos(tiltAngle + yFov / 2) / (1 / Math.cos(tiltAngle - yFov / 2)), 1 / nY ); // Creating the X and Y pixel boundary arrays const beta = Math.atan( (Math.tan(xFov / 2) * (1 / Math.cos(yFov / 2 + tiltAngle) - 1 / Math.cos(yFov / 2 - tiltAngle))) / (Math.tan(tiltAngle + yFov / 2) - Math.tan(tiltAngle - yFov / 2)) ); const initXArray = Array.from( { length: nX + 1 }, (_, i) => -width1 / 2 + (width1 / nX) * i ); const spacingInit = (width1 * (totalScale - 1)) / (2 * Math.tan(beta)); const yArray = new Array(nY + 1).fill(0); const xArray = new Array(nY + 1) .fill(null) .map(() => new Array(nX + 1).fill(0)); xArray[0] = initXArray.map((x) => x + xIR); // create the x and y pixel arrays for (let yIndex = 0; yIndex < nY; yIndex++) { yArray[yIndex + 1] = yArray[yIndex] + spacingInit * Math.pow(totalScale, yIndex); xArray[yIndex + 1] = initXArray.map( (x) => x * Math.pow(totalScale, yIndex + 1) + xIR ); } const YArrayShifted = yArray.map((y) => y + YBound1); // make this array the same size as numpy const yArrayExpanded = Array(nX + 1) .fill(null) .map((_, i) => YArrayShifted); return xArray.map((row, index) => row.map((x, i) => [x, yArrayExpanded[index][index]]) ); }3a:T4e9,//NaN handling function plotRows(array) { let lines = []; for (let i = 0; i < array.length; i++) { let startX, endX; // Find the first and last defined values in the row for (let j = 0; j < array[i].length; j++) { if (array[i][j] !== undefined) { startX = array[i][j]; break; } } for (let j = array[i].length - 1; j >= 0; j--) { if (array[i][j] !== undefined) { endX = array[i][j]; break; } } // Only add a line if both startX and endX are defined if (startX && endX) { lines.push({ p1: [startX[0], startX[1]], p2: [endX[0], endX[1]] }); } } return lines; } // function plotRows(array) { // // Create an array to hold all line data // let lines = []; // // Loop through each row in ir_center // for (let i = 0; i < array.length; i++) { // // Define start and end points for the line // let startX = array[i][0]; // let endX = array[i][array[i].length - 1]; // // Push line data to the array // lines.push({ // type: "line", // p1: [startX[0], startX[1]], // p2: [endX[0], endX[1]], // stroke: "black", // strokeWidth: 2 // }); // } // return lines; // }3b:T420,// NaN handling function plotCols(array) { let lines = []; for (let j = 0; j < array[0].length; j++) { let startY, endY; // Find the first and last defined values in the column for (let i = 0; i < array.length; i++) { if (array[i][j] !== undefined) { startY = array[i][j]; break; } } for (let i = array.length - 1; i >= 0; i--) { if (array[i][j] !== undefined) { endY = array[i][j]; break; } } // Only add a line if both startY and endY are defined if (startY && endY) { lines.push({ p1: [startY[0], startY[1]], p2: [endY[0], endY[1]] }); } } return lines; } // function plotCols(array) { // let lines = []; // for (let j = 0; j < array[0].length; j++) { // let startY = array[0][j]; // let endY = array[array.length - 1][j]; // lines.push({ // p1: [startY[0], startY[1]], // p2: [endY[0], endY[1]], // stroke: "black", // strokeWidth: 2 // }); // } // return lines; // }3c:[] 32:{"id":"e59adcda579dcbb1","slug":"infrared-sensor-transform-utility","title":"Infrared Sensor Transform Utility","thumbnail":"2c972d1a502a66b447754e8546aae5b6d60d0d7bdf0fc42ada4f4863e47f61db","access_level":"unlisted","create_time":"$D2024-09-09T22:13:34.989Z","update_time":"$D2025-02-04T15:00:20.347Z","view_time":null,"first_public_time":null,"has_unpublished_edits":null,"fork":true,"stars":0,"starred":false,"owner":{"type":"team","id":"abfd2a4c021d66ca","login":"nikolaiteslovich","name":"Nikolai Nekrutenko","avatar_url":"https://avatars-next.observableusercontent.com/0bafa58e62c1f685eb831aeb2f011622aa0bb254e8e7c84fff49f040b5a58b1c","tier":"starter_2024"},"version":914,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"cf28f71ca8e6a61b","login":"nikolaiteslovich","name":"Nikolai Nekrutenko","avatar_url":"https://avatars-next.observableusercontent.com/0bafa58e62c1f685eb831aeb2f011622aa0bb254e8e7c84fff49f040b5a58b1c","tier":null}],"members":[{"type":"individual","id":"cf28f71ca8e6a61b","login":"nikolaiteslovich","name":"Nikolai Nekrutenko","avatar_url":"https://avatars-next.observableusercontent.com/0bafa58e62c1f685eb831aeb2f011622aa0bb254e8e7c84fff49f040b5a58b1c","tier":null,"role":"editor"},{"type":"team","id":"abfd2a4c021d66ca","login":"nikolaiteslovich","name":"Nikolai Nekrutenko","avatar_url":"https://avatars-next.observableusercontent.com/0bafa58e62c1f685eb831aeb2f011622aa0bb254e8e7c84fff49f040b5a58b1c","tier":"starter_2024","role":"viewer"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"title":"Infrared Sensor Transform Utility","cells":[{"id":0,"value":"# Infrared Sensor Transform Utility","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":586,"value":"## IR Sensor to Target Surface Visualization\n${textcolor('IR Sensor Pixels in Blue', \"steelblue\")} ${textcolor('Hotplate Thermocouples in Red', \"#d1615d\")}","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":186,"value":"$34","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":479,"value":"### IR Sensor Parameters\n\nNote the values loaded by default are for a 24 by 32 pixel thermal sensor that is imaging a square-shaped surface offset by 0.25m in Z, -0.10m in Y and 0.00m in X with a tilt angle of 20 degrees. ","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":405,"value":"viewof tilt = Inputs.range([0, 45], {\n value: 22.412,\n step: 0.1,\n label: \"tilt [deg]\"\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":441,"value":"viewof ir_coords = Inputs.form([\n Inputs.range([-0.5, 0.5], { value: 0, step: 0.005, label: \"x [m]\" }),\n Inputs.range([-0.5, 0.5], { value: -0.1, step: 0.005, label: \"y [m]\" }),\n Inputs.range([0, 1], { value: 0.25, step: 0.005, label: \"z [m]\" })\n])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":466,"value":"viewof ir_fov = Inputs.form([\n Inputs.range([10, 120], {\n value: 55,\n step: 1,\n label: \"x field of view [deg]\"\n }),\n Inputs.range([10, 120], {\n value: 35,\n step: 1,\n label: \"y field of view [deg]\"\n })\n])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":675,"value":"viewof n_x = Inputs.range([n_y, 100], {\n value: 32,\n step: 1,\n label: \"# x pixels\"\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":678,"value":"viewof n_y = Inputs.range([4, 100], { value: 24, step: 1, label: \"# y pixels\" })","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":502,"value":"### Target Surface Parameters","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":505,"value":"viewof tc_dimensions = Inputs.form([\n Inputs.range([0.1, 0.5], { value: 0.2, step: 0.01, label: \"x width (m)\" }),\n Inputs.range([0.1, 0.5], { value: 0.2, step: 0.01, label: \"y height (m)\" })\n])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":511,"value":"viewof tc_resolution = Inputs.form([\n Inputs.range([2, 10], {\n value: 3,\n step: 1,\n label: \"# x temperature sensors\"\n }),\n Inputs.range([2, 10], { value: 3, step: 1, label: \"# y temperature sensors\" })\n])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":589,"value":"---\n\n## Mathematical Methods Documentation\n\nFor the figures below, the X-axis POV is analogous to looking at the IR camera experimental setup from one of the sides, and the Y-axis POV is looking at the IR camera experimental setup head-on.\n","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":619,"value":"html`\n \n \n \n \n \n \n \n \n

Fig. 1: IR Sensor Experimental Setup (X-axis POV)	Fig. 2: IR Sensor Experimental Setup (Y-axis POV)
$\"IR$	$\"IR$

`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":637,"value":"$35","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":595,"value":"### Variable Definitions\n- ${tex`\\theta`}: tilt angle of the sensor relative to the z-axis\n- ${tex`n_x`}: # of pixels in the x-axis\n- ${tex`n_y`}: # of pixels in the y-axis\n- ${tex`\\phi_x`}: x-axis field of view (FOV)\n- ${tex`\\phi_y`}: y-axis field of view (FOV)\n- ${tex`{l}_0`}: length in x of the smallest base of the isoceles trapezoid\n- ${tex`{y}_0`}: starting y-axis coordinate of the smallest base of the isoceles trapezoid\n- ${tex`s_{factor}`}: scaling factor per row iteration, multiplicative constant by which the row spacing above is larger than the row below\n- ${tex`s_{init}`}: initial y-axis spacing between rows, this increases by ${tex`s_{factor}`} every time\n- ${tex`\\beta`}: angle of spread of the isoceles trapezoid. For instance, if the sensor is facing the target surface overhead, the projected image would be a square and ${tex`\\beta`} would be zero. If the sensor is directly parallel to the target surface? (${tex`\\theta`} = 90°), then ${tex`\\beta = \\phi_x`}","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":642,"value":"$36","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":657,"value":"$37","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":857,"value":"### Calculating Pixel Boundaries vs Pixel Centers\n\nAll of the mathematical derivations above are for pixel boundary coordinate calculations. For the pixel centers, the variables are artificially modified before going into the function as such:\n\n```\ndef pixels_proj_arr(pos_list, fov_list, tilt, resolution):\n pixel_comp_fov_list = [0, 0]\n pixel_comp_resolution = [0, 0]\n for i in range(2):\n pixel_comp_fov_list[i] = np.rad2deg(2 * np.arctan(((resolution[i] - 1)/resolution[i]) \n * np.tan(np.deg2rad(fov_list[i] / 2))))\n pixel_comp_resolution[i] = resolution[i] - 1\n return boundaries_proj_arr(pos_list, pixel_comp_fov_list, tilt, pixel_comp_resolution)\n```\n\n---\n\nLet the JavaScript begin:","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":744,"value":"import { textcolor } from \"@observablehq/text-color-annotations-in-markdown\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":93,"value":"ir_bound = boundariesProjArr(ir_coords, ir_fov, tilt, [n_x, n_y])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":139,"value":"ir_center = pixelsProjArr(ir_coords, ir_fov, tilt, [n_x, n_y])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":18,"value":"$38","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":144,"value":"function tcCentersProjArr(TCDimensions, TCResolution) {\n // pulling data from the input lists to the arrays\n const nX = TCResolution[0] - 1;\n const nY = TCResolution[1] - 1;\n\n const widthX = TCDimensions[0] * (nX / (nX + 1));\n const heightY = TCDimensions[1] * (nY / (nY + 1));\n\n // Create X and Y arrays using linspace equivalent\n const xArray = Array.from(\n { length: nX + 1 },\n (_, i) => -widthX / 2 + (widthX / nX) * i\n );\n const yArray = Array.from(\n { length: nY + 1 },\n (_, i) => -heightY / 2 + (heightY / nY) * i\n );\n\n // Create meshgrid\n const meshgridX = [];\n const meshgridY = [];\n\n for (let i = 0; i <= nY; i++) {\n const rowX = [];\n const rowY = [];\n for (let j = 0; j <= nX; j++) {\n rowX.push(xArray[j]);\n rowY.push(yArray[i]);\n }\n meshgridX.push(rowX);\n meshgridY.push(rowY);\n }\n\n // Stack the meshgrid arrays along a new axis\n const stackedArray = meshgridX.map((rowX, i) =>\n rowX.map((x, j) => [x, meshgridY[i][j]])\n );\n\n return stackedArray;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":16,"value":"$39","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":127,"value":"function pixelsProjArr(posList, fovList, tilt, resolution) {\n let pixelCompFovList = [0, 0];\n let pixelCompResolution = [0, 0];\n\n for (let i = 0; i < 2; i++) {\n pixelCompFovList[i] =\n 2 *\n Math.atan(\n ((resolution[i] - 1) / resolution[i]) *\n Math.tan(toRadians(fovList[i] / 2))\n ) *\n (180 / Math.PI);\n pixelCompResolution[i] = resolution[i] - 1;\n }\n\n return boundariesProjArr(\n posList,\n pixelCompFovList,\n tilt,\n pixelCompResolution\n );\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":129,"value":"function toRadians(degrees) {\n return degrees * (Math.PI / 180);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":22,"value":"tc_bound = tcBoundariesProjArr(tc_dimensions, tc_resolution)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":153,"value":"tc_center = tcCentersProjArr(tc_dimensions, tc_resolution)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":39,"value":"function dataGraph(data) {\n function sliceArray(arr, index) {\n return arr.map((row) => row.map((col) => col[index]));\n }\n\n const data_x = sliceArray(data, 0);\n const data_y = sliceArray(data, 1);\n\n // Flatten the 2D arrays and pair x and y values\n const plotData = data_x.flatMap((row, i) =>\n row.map((x, j) => ({ x: x, y: data_y[i][j] }))\n );\n\n return plotData;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":61,"value":"plot_tc_center = dataGraph(tc_center)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":168,"value":"plot_tc_bound = dataGraph(tc_bound)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":97,"value":"plot_ir_center = dataGraph(ir_center)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":173,"value":"plot_ir_bound = dataGraph(ir_bound)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":226,"value":"// Function to plot bound lines\nfunction plotBoundLines(\n xArray,\n yArray,\n color = \"orange\",\n strokeWidth = 1,\n opacity = 0.6\n) {\n const lines = [];\n\n // Plot row lines\n for (let i = 0; i < yArray.length; i++) {\n for (let j = 0; j < xArray[i].length - 1; j++) {\n lines.push({\n x1: xArray[i][j],\n y1: yArray[i][j],\n x2: xArray[i][j + 1],\n y2: yArray[i][j + 1]\n });\n }\n }\n\n // Plot column lines\n for (let j = 0; j < xArray[0].length; j++) {\n for (let i = 0; i < yArray.length - 1; i++) {\n lines.push({\n x1: xArray[i][j],\n y1: yArray[i][j],\n x2: xArray[i + 1][j],\n y2: yArray[i + 1][j]\n });\n }\n }\n\n return Plot.line(lines, {\n x1: \"x1\",\n y1: \"y1\",\n x2: \"x2\",\n y2: \"y2\",\n stroke: color,\n strokeWidth: strokeWidth,\n opacity: opacity\n });\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":265,"value":"$3a","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":283,"value":"$3b","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":272,"value":"ir_cols_plot = plotCols(ir_bound)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":278,"value":"ir_rows_plot = plotRows(ir_bound)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":365,"value":"tc_rows_plot = plotRows(tc_bound)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":367,"value":"tc_cols_plot = plotCols(tc_bound)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":192,"value":"// Function to generate line segments between consecutive points in rows\nfunction createRowLines(data) {\n const lines = [];\n const groupedByY = d3.group(data, (d) => d.y);\n for (const [y, points] of groupedByY) {\n points.sort((a, b) => a.x - b.x);\n for (let i = 0; i < points.length - 1; i++) {\n lines.push({\n x1: points[i].x,\n y1: points[i].y,\n x2: points[i + 1].x,\n y2: points[i + 1].y\n });\n }\n }\n return lines;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":196,"value":"// Function to generate line segments between consecutive points in columns\nfunction createColumnLines(data) {\n const lines = [];\n const groupedByX = d3.group(data, (d) => d.x);\n for (const [x, points] of groupedByX) {\n points.sort((a, b) => a.y - b.y);\n for (let i = 0; i < points.length - 1; i++) {\n lines.push({\n x1: points[i].x,\n y1: points[i].y,\n x2: points[i + 1].x,\n y2: points[i + 1].y\n });\n }\n }\n return lines;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W3c","stdlib":"1","titling":"auto"}} 33:"$32:body"