Computer Graphics & Visualization @ufrj.br
Canvas primerCanvas primer IISVG IntroMinimal WebGL ProgramWebGL primer with reglShadertoy style drawingTransformation demoModelview DemoModel, View and Projection DemoWebGL CubeCatmull Clark SubdivisionThree.js basicsPhong Illumination modelHalf-edge data structureIterated Function SystemsRaytracingTextured sphereEnvironment mappingPhysical animation with shape matchingShape matching2D GJK and EPA algorithmsOmohundro balltree construction algorithmsPlatonic Solids PlaygroundElliptic billiards 3-periodics in space-time3D LabyrinthBrush drawingBump mappingFractal TerrainModel viewerKeyframe animationTextured planeSimple Adaptive Mosaic EffectsWallpaper GroupsRay marchingVolume rendering with slice compositingDisplaying 3D RBFs with ray marchingRandom space-filling curvesGPU-IO3D Apollonian Sphere PackingsCircle inversion fractalsApollonian gasket construction by inversionSmooth PolygonDocument image segmentationB-SplinesStencil bufferNoise LoopsSimplex noise exerciserDeformation with RBFsRandom shapes in a gridHobby curvesLane-Riesenfeld subdivision
Funções 2D úteis
import { vec2, mat3 } from "@esperanc/vec2-utils"
function dist([x0, y0], [x1, y1]) {
return Math.hypot(x1 - x0, y1 - y0);
}
dist([1, 1], [2, 2])
vec2.distance([1, 1], [2, 2])
function orient(a, b, c) {
return Math.sign(
mat3.determinant([1, a[0], a[1], 1, b[0], b[1], 1, c[0], c[1]])
);
}
orient([1, 1], [2, 2], [2, 1])
orient([1, 1], [2, 2], [1, 2])
orient([1, 1], [2, 2], [3, 3])
vec2.orient([1, 1], [2, 2], [1, 2])
function segmentsIntersect(a, b, c, d) {
return (
Math.abs(orient(a, b, c) - orient(a, b, d)) >= 1 &&
Math.abs(orient(c, d, a) - orient(c, d, b)) >= 1
);
}
function segmentsIntersectProper(a, b, c, d) {
return (
Math.abs(orient(a, b, c) - orient(a, b, d)) == 2 &&
Math.abs(orient(c, d, a) - orient(c, d, b)) == 2
);
}
segmentsIntersect([0, 0], [2, 2], [2, 2], [2, 0])
segmentsIntersectProper([0, 0], [2, 2], [2, 2], [2, 0])
function pointInConvexPoly(p, poly) {
let prevPoint = poly[poly.length - 1];
let prevOrient = 0;
for (let q of poly) {
const o = orient(prevPoint, q, p);
if (Math.abs(o - prevOrient) > 1) return false;
prevOrient = o;
prevPoint = q;
}
return true;
}
pointInConvexPoly(
[2, 2],
[
[-1, -1],
[1, 0],
[0, 1]
]
)
function lineLineIntersection(p1, v1, p2, v2) {
const D = v1[0] * v2[1] - v1[1] * v2[0];
const t = (v2[1] * (p2[0] - p1[0]) + p1[1] * v2[0] - p2[1] * v2[0]) / D;
return [p1[0] + v1[0] * t, p1[1] + v1[1] * t];
}
function vectorProj(u, v) {
const vnorm = vec2.normalize([], v);
return vec2.scale([], vnorm, vec2.dot(vnorm, u));
}
vectorProj([1, 1], [10, 0])
function distToLine(q, p, v) {
const pq = vec2.sub([], q, p);
const pqProj = vectorProj(pq, v);
return vec2.len(vec2.sub([], pq, pqProj));
}
function distToSegment(p, a, b) {
const v = vec2.sub([], b, a);
const vlen = dist(a, b);
const vnorm = vec2.scale([], v, 1 / vlen);
const ap = vec2.sub([], p, a);
const t = vec2.dot(vnorm, ap);
if (t < 0) return dist(p, a);
if (t > vlen) return dist(p, b);
return vec2.len(vec2.sub([], ap, vec2.scale([], vnorm, t)));
}
function polygonArea(poly) {
let [px, py] = poly[poly.length - 1];
let area = 0;
for (let [x, y] of poly) {
area += (px - x) * (y + py);
[px, py] = [x, y];
}
return area / 2;
}
function barycentric(p, a, b, c) {
const A = polygonArea([a, b, c]);
return [
polygonArea([a, b, p]) / A,
polygonArea([b, c, p]) / A,
polygonArea([c, a, p]) / A
];
}
function pointInPoly(p, poly) {
// The y coordinate of p
const py = p[1];
// 1d orientation of a point's y with respect to py
const yOrient = (p) => Math.sign(p[1] - py);
// Number of vertices
const n = poly.length;
// Previous point (the last of poly) and its y orientation
let prev = poly[n - 1];
let prevYOr = yOrient(prev);
// Intersection counter
let count = 0;
// Test all vertices
for (let i = 0; i < n; i++) {
const q = poly[i];
const yOr = yOrient(q);
if (Math.abs(yOr - prevYOr) >= 1) {
// Point within y range of segment prev-q
const pOr = orient(prev, q, p);
const far = [Math.max(prev[0], q[0]) * 2, py]; // Point to the right of segment prev-q
const farOr = orient(prev, q, far);
if (Math.abs(pOr - farOr) == 2) {
// segment p-far crosses segment prev-q
if (yOr == 0) {
// Intersection at q ?
// Test if next endPoint on opposite y orientations
const next = poly[(i + 1) % n];
const nextYOr = yOrient(next);
if (Math.abs(nextYOr - prevYOr) == 2) count++;
} else {
if (prevYOr != 0) count++; // Ignore intersections passing through prev
}
}
}
prevYOr = yOr;
prev = q;
}
return count % 2 == 1;
}
util2d = ({
dist,
orient,
segmentsIntersect,
segmentsIntersectProper,
pointInConvexPoly,
lineLineIntersection,
vectorProj,
distToLine,
distToSegment,
polygonArea,
barycentric,
pointInPoly
})
One platform to build and deploy the best data apps
Experiment and prototype by building visualizations in live JavaScript notebooks. Collaborate with your team and decide which concepts to build out.
Use Observable Framework to build data apps locally. Use data loaders to build in any language or library, including Python, SQL, and R.
Seamlessly deploy to Observable. Test before you ship, use automatic deploy-on-commit, and ensure your projects are always up-to-date.