// 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 = [];
+ // We tack [1,0,0] onto the end as a hack to see where
+ // it ends up after rotation. This is removed later.
+ var loop = shape.concat([[1,0,0]]);
+
// 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]));
+ // becomes shapenormals[i]. This puts the shape in
+ // the correct plane, but does not constrain its
+ // rotation about shapenormals[i].
+ loop = this.rotate_onto(loop, [0,0,1], shapenormals[i]);
+ var shapex = loop.pop();
+
// 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
+ loop = this.rotate_onto(loop, shapex, fixedpathnormals[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;
- }
+ // rather than separate steps.)
+
+ // 3. Translate to path[i].
+ loop = this.translate(loop, path[i]);
+
if (i == 0) {
result.first_loop = loop;
} else {
a[1] - b[1],
a[2] - b[2]];
},
+ neg: function(a) {
+ return [-a[0], -a[1], -a[2]];
+ },
dot: function(a, b) {
return a[0]*b[0] + a[1]*b[1] + a[2]*b[2];
},
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]];
+ translate: function(points, offset) {
+ var translated = [];
+ for (var i = 0; i < points.length; i++) {
+ translated[i] = [points[i][0] + offset[0],
+ points[i][1] + offset[1],
+ points[i][2] + offset[2]];
+ }
+ return translated;
},
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
+ rotate_about_origin: function(points, 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];
+ var rotated = [];
+ for (var i = 0; i < points.length; i++) {
+ var p = points[i];
+ var tmp = this.dot(p, axis) * (1 - cosangle);
+ rotated[i] = [
+ axis[0]*tmp + p[0]*cosangle + (-axis[2]*p[1] + axis[1]*p[2])*sinangle,
+ axis[1]*tmp + p[1]*cosangle + ( axis[2]*p[0] - axis[0]*p[2])*sinangle,
+ axis[2]*tmp + p[2]*cosangle + (-axis[1]*p[0] + axis[0]*p[1])*sinangle];
+ }
+ return rotated;
+ },
+ rotate_onto: function(points, a, b) {
+ // Rotate points such that a (in points-space) maps onto b
+ // by crossing a and b to get a rotation axis and using
+ // angle_between to get a rotation angle.
+ var angle = this.angle_between(this.unit(a), this.unit(b));
+ if (Math.abs(angle) < 1e-15) {
+ // No siginificant rotation to perform. Bail to avoid
+ // NaNs and numerical error
+ return points;
+ }
+ var axis = this.unit(this.cross(a, b));
+ return this.rotate_about_origin(points, axis, angle);
+ },
+ rotate: function(points, center, axis, angle) { // axis must be a unit vector
+ return this.translate(
+ this.rotate_about_origin(
+ this.translate(points, this.neg(center)),
+ axis,
+ angle),
+ center);
},
go: function() {
+ // Remove any previous download links
+ var old_download_link = document.getElementById("nt3d_download");
+ if (old_download_link) {
+ old_download_link.parentNode.removeChild(old_download_link);
+ }
+
+ // Continue in a callback, so that there's not a stale download
+ // link hanging around while we process.
+ setTimeout(function(the_this) { (function() {
+
// Get params from form
var params = [];
for (var i = 0; i < this.user_params.length; i++) {
- params[i] = this.form.elements["param"+i].value;
+ var as_string = this.form.elements["param"+i].value;
+ var as_num = +as_string;
+ params[i] = isNaN(as_num) ? as_string : as_num;
}
// Run user_function
}
this.stl += "endsolid " + this.user_function.name + "\n";
- // Remove any previous download links
- var old_download_link = document.getElementById("nt3d_download");
- if (old_download_link) {
- old_download_link.parentNode.removeChild(old_download_link);
- }
// Offer result as download
var download_link = document.createElement("a");
download_link.setAttribute("href", "data:application/sla," + encodeURIComponent(this.stl));
this.ui.appendChild(download_link);
setTimeout(function() { download_link.setAttribute("style", "-webkit-transition: background-color 0.4s; -moz-transition: background-color 0.4s; -o-transition: background-color 0.4s; -ms-transition: background-color 0.4s; transition: background-color 0.4s; background-color: inherit"); }, 0);
+
+ }).call(the_this); }, 0, this); // (We were in a callback this whole time, remember?)
},
framework: function (f, params) {
this.user_function = f;
projects / nt3d / blobdiff