Add orthographic cameras.

Orthographic cameras are specified by setting the `orthographic` attribute of the `<camera>` element. The `fovy` attribute is still used to specify the field-of-view, but its semantic is different for orthographic cameras. For orthographic cameras, the field-of-view is expressed in units of length, rather than degrees.

Other related changes:

* Fix bug in the ordering of `cam_xxx` elements in `mjModel`.
* Make camera visualization translucent only when the frustum is visualized.
* Added a button to `simulate` to toggle between perspective and orthographic free cameras.

https://youtu.be/ZXBTEIDWHhs

PiperOrigin-RevId: 642293435
Change-Id: Id090a421ad88ab404b5b27ddbbd6bfc81ad49bc5

src/engine/engine_vis_interact.c

@@ -223,16 +223,29 @@ void mjv_cameraInRoom(mjtNum* headpos, mjtNum* forward, mjtNum* up, const mjvSce
 
 // get frustum height at unit distance from camera; average left and right OpenGL cameras
 mjtNum mjv_frustumHeight(const mjvScene* scn) {
-  mjtNum height;
+  const mjvGLCamera* cam1 = scn->camera;
+  const mjvGLCamera* cam2 = scn->camera + 1;
 
-  // check znear
-  if (scn->camera[0].frustum_near < mjMINVAL || scn->camera[1].frustum_near < mjMINVAL) {
-    mjERROR("mjvScene frustum_near too small");
+  if (cam1->orthographic != cam2->orthographic) {
+    mjERROR("cannot average frustums of perspective and orthographic cameras");
   }
 
-  // add normalized height for left and right cameras
-  height = (scn->camera[0].frustum_top-scn->camera[0].frustum_bottom)/scn->camera[0].frustum_near +
-           (scn->camera[1].frustum_top-scn->camera[1].frustum_bottom)/scn->camera[1].frustum_near;
+  // get height
+  mjtNum height;
+  if (!cam1->orthographic) {
+    // check znear
+    if (cam1->frustum_near < mjMINVAL || cam2->frustum_near < mjMINVAL) {
+      mjERROR("mjvScene frustum_near too small");
+    }
+
+    // add normalized height for left and right cameras
+    height = (cam1->frustum_top - cam1->frustum_bottom) / cam1->frustum_near +
+             (cam2->frustum_top - cam2->frustum_bottom) / cam2->frustum_near;
+  } else {
+    // add height for left and right cameras
+    height = (cam1->frustum_top - cam1->frustum_bottom) +
+             (cam2->frustum_top - cam2->frustum_bottom);
+  }
 
   // average
   return 0.5*height;
@@ -337,6 +350,9 @@ void mjv_moveCamera(const mjModel* m, int action, mjtNum reldx, mjtNum reldy,
     mju_sub3(dif, cam->lookat, headpos);
     scl = mjv_frustumHeight(scn) * mju_dot3(dif, forward);
 
+    // multiply by mystery coefficient TODO: b/346130949
+    if (cam->orthographic) scl *= 0.15;
+
     // move lookat point in opposite direction
     mju_addToScl3(cam->lookat, vec, -scl);
     break;
@@ -563,6 +579,9 @@ void mjv_initPerturb(const mjModel* m, mjData* d, const mjvScene* scn, mjvPertur
   mju_sub3(dif, pert->refselpos, headpos);
   pert->scale = mjv_frustumHeight(scn) * mju_dot3(dif, forward);
 
+  // multiply by mystery coefficient TODO: b/346130949
+  if (scn->camera[0].orthographic) pert->scale *= 0.15;
+
   mj_freeStack(d);
 }
 
@@ -733,6 +752,12 @@ mjvGLCamera mjv_averageCamera(const mjvGLCamera* cam1, const mjvGLCamera* cam2)
   cam.frustum_near   = 0.5f * (cam1->frustum_near + cam2->frustum_near);
   cam.frustum_far    = 0.5f * (cam1->frustum_far + cam2->frustum_far);
 
+  if (cam1->orthographic != cam2->orthographic) {
+    mjERROR("cannot average perspective and orthographic cameras");
+  } else {
+    cam.orthographic = cam1->orthographic;
+  }
+
   return cam;
 }
 
@@ -755,17 +780,31 @@ int mjv_select(const mjModel* m, const mjData* d, const mjvOption* vopt,
   // compute frustum halfwidth so as to match viewport aspect ratio
   mjtNum halfwidth = 0.5*aspectratio*(cam.frustum_top - cam.frustum_bottom);
 
-  // construct ray
+  // compute up and left offsets from normalized cursor
+  mjtNum d_up = cam.frustum_bottom + rely*(cam.frustum_top-cam.frustum_bottom);
+  mjtNum d_left = -(cam.frustum_center + (2*relx-1)*halfwidth);
+
+  // define ray
   mjtNum ray[3];
-  mju_scl3(ray, forward, cam.frustum_near);
-  mju_addToScl3(ray, up, cam.frustum_bottom + rely*(cam.frustum_top-cam.frustum_bottom));
-  mju_addToScl3(ray, left, -(cam.frustum_center + (2*relx-1)*halfwidth));
-  mju_normalize3(ray);
+
+  // construct ray for orthographic camera: fixed direction, modify pos
+  if (cam.orthographic) {
+    mju_copy3(ray, forward);
+    mju_addToScl3(pos, up, d_up);
+    mju_addToScl3(pos, left, d_left);
+  }
+
+  // construct ray for perspective camera: fixed pos, modify direction
+  else {
+    mju_scl3(ray, forward, cam.frustum_near);
+    mju_addToScl3(ray, up, d_up);
+    mju_addToScl3(ray, left, d_left);
+    mju_normalize3(ray);
+  }
 
   // find intersection with geoms
   *geomid = -1;
-  mjtNum geomdist = mj_ray(m, d, pos, ray, vopt->geomgroup,
-                           vopt->flags[mjVIS_STATIC], -1, geomid);
+  mjtNum geomdist = mj_ray(m, d, pos, ray, vopt->geomgroup, vopt->flags[mjVIS_STATIC], -1, geomid);
 
   // find intersection with flexes
   int flexbodyid = -1;
@@ -851,7 +890,6 @@ int mjv_select(const mjModel* m, const mjData* d, const mjvOption* vopt,
     }
   }
 
-
   // geom
   if (best == 0) {
     *flexid = -1;