Sphere primitive

[nt3d] / nt3d.js

diff --git a/nt3d.js b/nt3d.js
index 9c4aeb18693000a43267508722918b30c6cdfe80..28766983fe33341b262ee572f4a09fc01d917d4c 100644 (file)
--- a/nt3d.js
+++ b/nt3d.js
@@ -62,6 +62,27 @@ nt3d = {
                return this.closed_trianglefan([apex].concat(base)).concat(
                       this.trianglefan(base.reverse()));
        },
+       sphere: function(center, radius, latitude_steps, longitude_steps) {
+               return this.oriented_sphere(center, radius, [0,0,1], [1,0,0], latitude_steps, longitude_steps);
+       },
+       oriented_sphere: function(center, radius, north, greenwich, latitude_steps, longitude_steps) {
+               var unit_north = this.unit(north);
+               var north_pole = this.translate_point(this.scale(unit_north,  radius), center);
+               var south_pole = this.translate_point(this.scale(unit_north, -radius), center);
+               return this.spheroid(north_pole, south_pole, radius, greenwich, latitude_steps, longitude_steps);
+       },
+       spheroid: function(north_pole, south_pole, radius, greenwich, latitude_steps, longitude_steps) {
+               var delta = this.sub(north_pole, south_pole);
+               var path = [];
+               for (var i = 0; i < latitude_steps-1; i++) {
+                       path.push(this.translate_point(south_pole, this.scale(delta, (1-Math.cos(Math.PI*i/(latitude_steps-1)))/2)));
+               }
+               path.push(north_pole);
+               function shape(i) {
+                       return nt3d.circle(radius*Math.sin(Math.PI*i/(latitude_steps-1)), longitude_steps);
+               }
+               return this.extrude(path, shape, delta, greenwich);
+       },
        shapenormals_from_closed_path: function(path) {
                return function(i) {
                        var prev = (i == 0) ? path.length-1 : i-1;
@@ -83,6 +104,14 @@ nt3d = {
                        return nt3d.sub(path[i+1], path[i-1]);
                };
        },
+       pathnormals_from_point: function(path, p) {
+               // Use this with any point that is not on any path tangent line
+               var pathnormals = [];
+               for (var i = 0; i < path.length; i++) {
+                       pathnormals.push(this.sub(path[i], p));
+               }
+               return pathnormals;
+       },
        to_function: function(thing, make_indexer) {
                // If thing is a point, just yield thing every time.
                // If thing is a list of points && make_indexer, index into thing.
@@ -98,19 +127,19 @@ nt3d = {
        },
        extrude: function(path, shape, shapenormals, pathnormals) {
 
-               var guts_result = nt3d._extrude_guts(path, shape, shapenormals, pathnormals);
+               var guts_result = this._extrude_guts(path, shape, 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));
+                       this.trianglefan(guts_result.first_loop.reverse()),
+                       this.trianglefan(guts_result.last_loop));
 
        },
        closed_extrude: function(path, shape, shapenormals, pathnormals) {
-               var guts_result = nt3d._extrude_guts(path, shape, shapenormals, pathnormals);
+               var guts_result = this._extrude_guts(path, shape, shapenormals, pathnormals);
                // Stitch the ends together
                return guts_result.points.concat(
-                       nt3d.closed_quadstrip(nt3d.zip(guts_result.first_loop, guts_result.last_loop)));
+                       this.closed_quadstrip(this.zip(guts_result.first_loop, guts_result.last_loop)));
        },
        _extrude_guts: function(path, shape, shapenormals, pathnormals) {
                var shape_fun = this.to_function(shape, false);
@@ -164,7 +193,7 @@ nt3d = {
                        if (i == 0) {
                                result.first_loop = loop;
                        } else {
-                               result.points = result.points.concat(nt3d.closed_quadstrip(nt3d.zip(loop, prev_loop)));
+                               result.points = result.points.concat(this.closed_quadstrip(this.zip(loop, prev_loop)));
                        }
                        prev_loop = loop;
                }
@@ -211,7 +240,7 @@ nt3d = {
        },
        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);
+               return this.scale(a, this.dot(a, b) / (a_magnitude * a_magnitude));
        },
        project_to_orthogonal: function(a, b) {
                // The nearest thing to b that is orthogonal to a
@@ -220,12 +249,15 @@ nt3d = {
        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]];
+                       translated[i] = this.translate_point(points[i], offset);
                }
                return translated;
        },
+       translate_point: function(point, offset) {
+               return [point[0] + offset[0],
+                       point[1] + offset[1],
+                       point[2] + offset[2]];
+       },
        angle_between: function(a, b) { // a and b must be unit vectors
                return Math.acos(this.dot(a, b));
        },