added motor orbit rendering example.

KILLTUBE · Mar 27, 2019 · 0ef912a · 0ef912a
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diff --git a/examples/coffeeshop.html b/examples/coffeeshop.html
@@ -287,7 +287,7 @@ <H3 STYLE="flex-grow:1" ID="title">The CoffeeShop</H3>
                     "timespace_lorentz",
                     "ga3d_rotor_estimation",
                     "pga2d_points_and_lines","pga2d_distances_and_angles","pga2d_project_and_reject","pga2d_rotors_and_translators","pga2d_isometries", "pga2d_inverse_kinematics","pga2d_separating_axis","pga2d_pose_estimation","pga2d_euler_line","pga2d_desargues_theorem","pga2d_differentiation","pga2d_physics_moon","pga2d_origami", "pga2d_poncelet",
-                    "pga3d_points_and_lines","pga3d_distances_and_angles","pga3d_rotors_and_translators","pga3d_icosahedron","pga3d_sampling","pga3d_slicing","pga3d_differentiation","pga3d_skinning","pga3d_physics_planets","pga3d_origami","pga3d_physics_symmetric_top","pga3d_physics_free_top","pga3d_objects","pga3d_levenberg_marquardt",
+                    "pga3d_points_and_lines","pga3d_distances_and_angles","pga3d_rotors_and_translators","pga3d_icosahedron","pga3d_sampling","pga3d_slicing","pga3d_differentiation","pga3d_skinning","pga3d_physics_planets","pga3d_origami","pga3d_physics_symmetric_top","pga3d_physics_free_top","pga3d_objects","pga3d_levenberg_marquardt","pga3d_motor_orbits",
                     "cga2d_points_and_circles","cga2d_project_and_reject","cga2d_rotors_and_translators","cga2d_euler_line",
                     "cga3d_points_circles_lines","cga3d_points_spheres_planes","cga3d_dual_spheres_planes","cga3d_intersections","cga3d_project_reject","cga3d_opns_visualizer","cga3d_opns_line_circle","cga3d_json",
                     "mga3d_points_and_lines",

diff --git a/examples/example_pga3d_motor_orbits.html b/examples/example_pga3d_motor_orbits.html
@@ -0,0 +1,49 @@
+<HEAD>
+  <SCRIPT SRC="../ganja.js"></SCRIPT>
+</HEAD>
+<BODY><SCRIPT>
+Algebra(3,0,1,()=>{
+
+  // Ganja.js can graph the orbits of parametrised motor variables :
+  // these are functions that take one parameter 0<x<1 and return a motor.
+  // For a function of 1 parameter, the orbit is rendered as a curve.
+
+  var circle  = (BV,r)=>x=>Math.E**(Math.PI*x*BV)*(1+r*.5e01),
+      segment = (BV)=>x=>1+x*0.5*BV;
+
+  // The product of two such parametrised 1D orbits is a 2D manifold :
+  // In ganja, you can simply multiply the two 1-parameter orbits to 
+  // make a 2-parameter manifold. (rendered as a sheet) 
+
+  // this allows us to multiply two circles into a torus or sphere,
+  // two segments into a plane, or a segment and a circle to produce
+  // a disk, cone or cylinder.
+
+  var torus    = (r1,r2)=>circle(1e12,r1)*circle(1e13,r2),
+      sphere   = (r)=>circle(1e13,0)*circle(1e12,r),
+      plane    = (x,y)=>segment(x*1e02)*segment(y*1e03),
+      cylinder = (r,l)=>segment(l*1e02)*circle(1e13,r),
+      disk     = (r)=>circle(1e12,0)*segment(r*1e01),
+      cone     = (r,l)=>circle(1e12,0)*segment(r*1e01-l*1e03);
+
+  // we can render these now just as our other primitives ..
+  var elements = [
+        0xff0000, circle(1e12,1),
+        0x0000ff, segment(1e01),
+        0xff0088, torus(.5,.2),
+        0xffff00, sphere(0.1),
+        0x00ffff, plane(0.2,0.2),
+        0x8800ff, cylinder(.05,1),
+        0x00ff00, disk(0.2),
+        0xffffff, cone(0.1,0.2)
+      ];
+
+  // show with rotating camera.. 
+  var camera=0e1+1;
+  document.body.appendChild(this.graph(()=>{
+    var t=performance.now()/1234; 
+    camera.set( Math.cos(t) + Math.sin(t)*1e13  );
+    return elements;
+  },{camera,gl:1,animate:1}));
+
+})</SCRIPT></BODY>
diff --git a/images/pga3d_motor_orbits.jpg b/images/pga3d_motor_orbits.jpg