opns cga example added

KILLTUBE · Nov 7, 2018 · f77ac8e · f77ac8e
1 parent 9ee4700
commit f77ac8e
Show file tree

Hide file tree

Showing 3 changed files with 40 additions and 1 deletion.
diff --git a/examples/coffeeshop.html b/examples/coffeeshop.html
@@ -184,7 +184,7 @@ <H3 STYLE="flex-grow:1" ID="title">The CoffeeShop</H3>
                     "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",
                     "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_points_circles_lines","cga3d_points_spheres_planes","cga3d_dual_spheres_planes","cga3d_intersections","cga3d_project_reject","cga3d_opns_line_circle",
                     "mga3d_points_and_lines",
                     "ccga3d_points_quadrics",
                     "qcga3d_points_and_more",

diff --git a/examples/example_cga3d_opns_line_circle.html b/examples/example_cga3d_opns_line_circle.html
@@ -0,0 +1,39 @@
+<HEAD>
+  <SCRIPT SRC="../ganja.js"></SCRIPT>
+</HEAD>
+<BODY><SCRIPT>
+// the OPNS visualizer can be used to visualize degenerate elements
+// for which the parametric form is unknown. It works by raytracing
+// a boundary on the length of the outer product.
+
+// We demonstrate in CGA. The OPNS visualizer only works for the graded
+// algebra generator, so we have to specify that when we create our algebra :
+Algebra({p:4,q:1,graded:true},()=>{
+
+  // As usual, we start by defining a null basis, and upcasting for points
+  var ni = 1e4+1e5, no = .5e5-.5e4, nino = ni^no;
+  var up = (x)=> no + x + .5*x*x*ni;
+
+  // for OPNS viz we also need an "up" version that uses only basis blades :
+  var upviz = ["x","y","z",".5*(x*x+y*y+z*z)-.5",".5*(x*x+y*y+z*z)+.5"];
+
+  // Next we create some points
+    var p1 = up(1e3-1e1), p2 = up(-1e3-1e1), p3 = up(1e2-1e1),
+        q1 = up(1e1+1e2), q2 = up(1e1-1e2);
+
+  // We create a circle and a line.
+    var c1 = (p1^p2^p3).Normalized, c2 = (p3^p2^ni).Normalized;
+
+  // Now we will use the OPNS visualizer to show how the shape of the
+  // object evolves as we interpolate from one to the other.
+    document.body.appendChild(this.graphGL2(()=>{
+       // factor between 0 and 1     
+       var t = Math.min(1,Math.max(0,0.5 + 0.75*Math.sin(performance.now()/700)));
+       // interpolate
+       var i = c1*t+(1-t)*c2;
+       // graph in pretty blue.
+       return [0x0088FF,i]
+    },{up:upviz, animate:1}))
+
+})
+</SCRIPT></BODY>
diff --git a/images/cga3d_opns_line_circle.jpg b/images/cga3d_opns_line_circle.jpg