From 3347946db76fa2d46309a2794658c01933e920d8 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Mikael=20L=C3=B6vqvist?= Date: Sun, 21 Dec 2025 20:39:47 +0100 Subject: [PATCH] Added rotating cube --- canvas/cube.js | 266 +++++++++++++++++++++++++++++++++++++++++++++++++ index.html | 1 + 2 files changed, 267 insertions(+) create mode 100644 canvas/cube.js diff --git a/canvas/cube.js b/canvas/cube.js new file mode 100644 index 0000000..1fd6f12 --- /dev/null +++ b/canvas/cube.js @@ -0,0 +1,266 @@ +// This file is mostly written by ChatGPT 5.2 + +// Renders 3D polylines (arrays of Vec3 points) onto a 2D canvas using a perspective frustum. +// - ctx: CanvasRenderingContext2D +// - polylines: Array> +// - camera: { +// eye:{x,y,z}, target:{x,y,z}, up:{x,y,z}, +// fovY:number (radians), aspect:number, near:number, far:number +// } +// - viewport: { x:number, y:number, w:number, h:number } // canvas rect in pixels + +function renderFrustumPolylines(ctx, polylines, camera, viewport) +{ + const V = mat4LookAt(camera.eye, camera.target, camera.up); + const P = mat4Perspective(camera.fovY, camera.aspect, camera.near, camera.far); + const VP = mat4Mul(P, V); + + ctx.beginPath(); + + for (const poly of polylines) + { + if (!poly || poly.length < 2) continue; + + for (let i = 0; i < poly.length - 1; i++) + { + const a = poly[i]; + const b = poly[i + 1]; + + const ca = mat4MulVec4(VP, [a.x, a.y, a.z, 1]); + const cb = mat4MulVec4(VP, [b.x, b.y, b.z, 1]); + + const clipped = clipLineClipSpace(ca, cb); + if (!clipped) continue; + + const [p0, p1] = clipped; + + // Perspective divide -> NDC + const ndc0 = [p0[0] / p0[3], p0[1] / p0[3], p0[2] / p0[3]]; + const ndc1 = [p1[0] / p1[3], p1[1] / p1[3], p1[2] / p1[3]]; + + // NDC [-1..1] -> screen pixels + const s0 = ndcToScreen(ndc0, viewport); + const s1 = ndcToScreen(ndc1, viewport); + + ctx.moveTo(s0[0], s0[1]); + ctx.lineTo(s1[0], s1[1]); + } + } + + ctx.stroke(); +} + +function ndcToScreen(ndc, vp) +{ + // Canvas y-axis points down; NDC y-axis points up. + const x = vp.x + (ndc[0] * 0.5 + 0.5) * vp.w; + const y = vp.y + (1 - (ndc[1] * 0.5 + 0.5)) * vp.h; + return [x, y]; +} + +// --- Homogeneous line clipping in clip space --- +// Clip space constraints (OpenGL-style): +// -w <= x <= w +// -w <= y <= w +// -w <= z <= w +// +// Returns null if fully outside, else returns [p0,p1] (both vec4 in clip space). +function clipLineClipSpace(p0, p1) +{ + let t0 = 0, t1 = 1; + const d = [p1[0] - p0[0], p1[1] - p0[1], p1[2] - p0[2], p1[3] - p0[3]]; + + // For each plane: (a·p + b >= 0). In homogeneous clip space: + // x + w >= 0, -x + w >= 0, y + w >= 0, -y + w >= 0, z + w >= 0, -z + w >= 0. + const planes = [ + [ 1, 0, 0, 1], // x + w >= 0 + [-1, 0, 0, 1], // -x + w >= 0 + [ 0, 1, 0, 1], // y + w >= 0 + [ 0, -1, 0, 1], // -y + w >= 0 + [ 0, 0, 1, 1], // z + w >= 0 + [ 0, 0, -1, 1] // -z + w >= 0 + ]; + + for (const pl of planes) + { + const f0 = pl[0]*p0[0] + pl[1]*p0[1] + pl[2]*p0[2] + pl[3]*p0[3]; + const f1 = pl[0]*p1[0] + pl[1]*p1[1] + pl[2]*p1[2] + pl[3]*p1[3]; + const df = f1 - f0; + + if (df === 0) + { + if (f0 < 0) return null; // parallel and outside + continue; + } + + const t = -f0 / df; + + if (df > 0) + { + // entering + if (t > t0) t0 = t; + } + else + { + // leaving + if (t < t1) t1 = t; + } + + if (t0 > t1) return null; + } + + const q0 = [ + p0[0] + d[0]*t0, p0[1] + d[1]*t0, p0[2] + d[2]*t0, p0[3] + d[3]*t0 + ]; + const q1 = [ + p0[0] + d[0]*t1, p0[1] + d[1]*t1, p0[2] + d[2]*t1, p0[3] + d[3]*t1 + ]; + + // Also reject if w is non-positive after clipping (avoid invalid perspective divide) + if (q0[3] <= 0 && q1[3] <= 0) return null; + + return [q0, q1]; +} + +// --- Minimal 4x4 matrix helpers (column-major, WebGL-style) --- + +function mat4Mul(A, B) +{ + // C = A * B + const C = new Float32Array(16); + for (let c = 0; c < 4; c++) + { + for (let r = 0; r < 4; r++) + { + C[c*4 + r] = + A[0*4 + r] * B[c*4 + 0] + + A[1*4 + r] * B[c*4 + 1] + + A[2*4 + r] * B[c*4 + 2] + + A[3*4 + r] * B[c*4 + 3]; + } + } + return C; +} + +function mat4MulVec4(M, v) +{ + return [ + M[0]*v[0] + M[4]*v[1] + M[8]*v[2] + M[12]*v[3], + M[1]*v[0] + M[5]*v[1] + M[9]*v[2] + M[13]*v[3], + M[2]*v[0] + M[6]*v[1] + M[10]*v[2] + M[14]*v[3], + M[3]*v[0] + M[7]*v[1] + M[11]*v[2] + M[15]*v[3] + ]; +} + +function mat4Perspective(fovY, aspect, near, far) +{ + const f = 1 / Math.tan(fovY * 0.5); + const nf = 1 / (near - far); + + const M = new Float32Array(16); + M[0] = f / aspect; M[4] = 0; M[8] = 0; M[12] = 0; + M[1] = 0; M[5] = f; M[9] = 0; M[13] = 0; + M[2] = 0; M[6] = 0; M[10] = (far + near) * nf; M[14] = (2 * far * near) * nf; + M[3] = 0; M[7] = 0; M[11] = -1; M[15] = 0; + return M; +} + +function mat4LookAt(eye, target, up) +{ + const z = normalize3(sub3(eye, target)); // forward (camera looks down -Z in view space) + const x = normalize3(cross3(up, z)); // right + const y = cross3(z, x); // true up + + const M = new Float32Array(16); + M[0] = x.x; M[4] = x.y; M[8] = x.z; M[12] = -dot3(x, eye); + M[1] = y.x; M[5] = y.y; M[9] = y.z; M[13] = -dot3(y, eye); + M[2] = z.x; M[6] = z.y; M[10] = z.z; M[14] = -dot3(z, eye); + M[3] = 0; M[7] = 0; M[11] = 0; M[15] = 1; + return M; +} + +// --- Vec3 helpers --- + +function sub3(a, b) { return { x: a.x - b.x, y: a.y - b.y, z: a.z - b.z }; } +function dot3(a, b) { return a.x*b.x + a.y*b.y + a.z*b.z; } +function cross3(a, b) +{ + return { + x: a.y*b.z - a.z*b.y, + y: a.z*b.x - a.x*b.z, + z: a.x*b.y - a.y*b.x + }; +} +function normalize3(v) +{ + const len = Math.hypot(v.x, v.y, v.z) || 1; + return { x: v.x / len, y: v.y / len, z: v.z / len }; +} + +function rotateVecY(v, angle) +{ + const c = Math.cos(angle); + const s = Math.sin(angle); + return { + x: v.x * c - v.z * s, + y: v.y, + z: v.x * s + v.z * c + }; +} + +function demo_cube() { + // Creates a cube centered at `center` with edge length `size`. + // Returns polylines compatible with renderFrustumPolylines(). + function createCubePolylines(center, size) + { + const h = size * 0.5; + + const v = [ + {x:center.x-h,y:center.y-h,z:center.z-h}, + {x:center.x+h,y:center.y-h,z:center.z-h}, + {x:center.x+h,y:center.y+h,z:center.z-h}, + {x:center.x-h,y:center.y+h,z:center.z-h}, + {x:center.x-h,y:center.y-h,z:center.z+h}, + {x:center.x+h,y:center.y-h,z:center.z+h}, + {x:center.x+h,y:center.y+h,z:center.z+h}, + {x:center.x-h,y:center.y+h,z:center.z+h} + ]; + + return [ + // bottom face + [v[0], v[1], v[2], v[3], v[0]], + // top face + [v[4], v[5], v[6], v[7], v[4]], + // vertical edges + [v[0], v[4]], + [v[1], v[5]], + [v[2], v[6]], + [v[3], v[7]] + ]; + } + + // Example usage: + const cube = createCubePolylines({x:0,y:0,z:0}, 1); + + const eye = rotateVecY({x:2,y:1,z:2}, performance.now()*0.001 % (Math.PI * 2)); + C.clearRect(0, 0, W, H); + + renderFrustumPolylines( + C, + cube, + { + eye, + target:{x:0,y:0,z:0}, + up:{x:0,y:1,z:0}, + fovY:Math.PI/4, + aspect:canvas.width/canvas.height, + near:0.1, + far:100 + }, + { x:0, y:0, w:canvas.width, h:canvas.height } + ); + + window.requestAnimationFrame(demo_cube); +} + +window.requestAnimationFrame(demo_cube); \ No newline at end of file diff --git a/index.html b/index.html index c607317..3a54667 100644 --- a/index.html +++ b/index.html @@ -15,6 +15,7 @@
  • Triangular lattice - sampling raster in a skewed pattern
  • Triangular lattice - unfinished interactive example
  • Image loading
    • +
  • Rotating cube