From: Scott Worley Date: Wed, 19 Dec 2012 04:45:50 +0000 (-0800) Subject: Extrusion X-Git-Url: http://git.scottworley.com/nt3d/commitdiff_plain/94faa4e58b86d3e6acdbe4f56d15d8fe21adf5c0 Extrusion --- diff --git a/box_by_extrude.html b/box_by_extrude.html new file mode 100644 index 0000000..e8183f2 --- /dev/null +++ b/box_by_extrude.html @@ -0,0 +1,24 @@ + + + Box by extrude + + + + +

Box by extrude

Make a box by extruding a square.

+ + diff --git a/nt3d.js b/nt3d.js index fbd8f50..d0d7161 100644 --- a/nt3d.js +++ b/nt3d.js @@ -46,11 +46,106 @@ nt3d = { closed_quadstrip: function(strip) { return this.quadstrip(strip.concat([strip[0], strip[1]])); }, + extrude: function(shape, path, shapenormals, pathnormals) { + var guts_result = nt3d._extrude_guts(shape, path, shapenormals, pathnormals); + // Add the end-caps + // XXX: This doesn't work if shape is not convex + return guts_result.points.concat( + nt3d.trianglefan(guts_result.first_loop.reverse()), + nt3d.trianglefan(guts_result.last_loop)); + + }, + closed_extrude: function(shape, path, shapenormals, pathnormals) { + var guts_result = nt3d._extrude_guts(shape, path, shapenormals, pathnormals); + // Stitch the ends together + return guts_result.points.concat( + nt3d.closed_quadstrip(nt3d.zip(guts_result.first_loop, guts_result.last_loop))); + }, + _fix_pathnormals: function(shapenormals, pathnormals) { + // Fix pathnormals[i] to be perfectly perpendicular to + // shapenormals[i]. This lets extrude callers be sloppy + // with pathnormals, which can greatly simplify things. + var fixedpathnormals = []; + for (var i = 0; i < pathnormals.length; i++) { + var proj = this.project(shapenormals[i], pathnormals[i]); + fixedpathnormals[i] = this.sub(pathnormals[i], proj); + } + return fixedpathnormals; + }, + _extrude_guts: function(shape, path, shapenormals, pathnormals) { + var fixedpathnormals = this._fix_pathnormals(shapenormals, pathnormals); + var result = { points: [] }; + var prev_loop; + for (var i = 0; i < path.length; i++) { + // loop is shape in 3d with (0,0) at path[i], shape's + // z axis in the direction of shapenormals[i], and + // shape's x axis in the direction of pathnormals[i]. + var loop = []; + // This is done in three steps: + // 1. Rotate shape out of the xy plane so that [0,0,1] + // becomes shapenormals[i] by crossing [0,0,1] and + // shapenormals[i] to get a rotation axis and taking + // their dot product to get a rotation angle. This + // puts the shape in the correct plane, but does not + // constrain its rotation about shapenormals[i]. + var rot1axis = this.unit(this.cross([0,0,1], shapenormals[i])); + var rot1angle = this.angle_between([0,0,1], this.unit(shapenormals[i])); + // 2. Rotate around shapenormals[i] so that [1,0,0] + // becomes fixedpathnormals[i]. + var rot2axis = this.unit(shapenormals[i]); + var rot2angle = this.angle_between([1,0,0], this.unit(fixedpathnormals[i])); + // 3. Translate to path[i]. + // This would probably be faster and more numerically stable + // if the two rotations were applied as one combined operation + // rather than separate steps. + for (var j = 0; j < shape.length; j++) { + var p = [shape[j][0], shape[j][1], 0]; + if (rot1angle > 1e-7) { + p = this.rotate(p, rot1axis, rot1angle); + } + if (rot2angle > 1e-7) { + p = this.rotate(p, rot2axis, rot2angle); + } + p = this.translate(p, path[i]); + loop[j] = p; + } + if (i == 0) { + result.first_loop = loop; + } else { + result.points = result.points.concat(nt3d.closed_quadstrip(nt3d.zip(loop, prev_loop))); + } + prev_loop = loop; + } + result.last_loop = prev_loop; + return result; + }, + zip: function(a, b) { + var result = []; + if (a.length != b.length) { + alert("Zip over different-sized inputs"); + } + for (var i = 0; i < a.length; i++) { + result.push(a[i], b[i]); + } + return result; + }, + magnitude: function(a) { + return Math.sqrt(a[0]*a[0] + a[1]*a[1] + a[2]*a[2]); + }, + unit: function(a) { + return this.scale(a, 1 / this.magnitude(a)); + }, sub: function(a, b) { return [a[0] - b[0], a[1] - b[1], a[2] - b[2]]; }, + dot: function(a, b) { + return a[0]*b[0] + a[1]*b[1] + a[2]*b[2]; + }, + scale: function(v, s) { // Scale vector v by scalar s + return [s*v[0], s*v[1], s*v[2]]; + }, cross: function(a, b) { return [a[1]*b[2] - a[2]*b[1], a[2]*b[0] - a[0]*b[2], @@ -59,6 +154,25 @@ nt3d = { normal: function(a, b, c) { return this.cross(this.sub(a, b), this.sub(b, c)); }, + project: function(a, b) { // Project b onto a + var a_magnitude = this.magnitude(a); + return this.scale(a, this.dot(a, b) / a_magnitude * a_magnitude); + }, + translate: function(a, b) { + return [a[0] + b[0], a[1] + b[1], a[2] + b[2]]; + }, + angle_between: function(a, b) { // a and b must be unit vectors + return Math.acos(this.dot(a, b)); + }, + rotate: function(point, axis, angle) { // axis must be a unit vector + // From http://inside.mines.edu/~gmurray/ArbitraryAxisRotation/ + var cosangle = Math.cos(angle); + var sinangle = Math.sin(angle); + var tmp = this.dot(point, axis) * (1 - cosangle); + return [axis[0]*tmp + point[0]*cosangle + (-axis[2]*point[1] + axis[1]*point[2])*sinangle, + axis[1]*tmp + point[1]*cosangle + ( axis[2]*point[0] - axis[0]*point[2])*sinangle, + axis[2]*tmp + point[2]*cosangle + (-axis[1]*point[0] + axis[0]*point[1])*sinangle]; + }, go: function() { // Get params from form var params = [];