Do spherical linear interpolation when we animate onto a workplane.

[git-p4: depot-paths = "//depot/solvespace/": change = 1722]

dsc.h

@@ -30,6 +30,8 @@ public:
     Vector RotationN(void);
     Vector Rotate(Vector p);
 
+    Quaternion ToThe(double p);
+    Quaternion Inverse(void);
     Quaternion Times(Quaternion b);
 };
 

graphicswin.cpp

@@ -158,9 +158,10 @@ void GraphicsWindow::AnimateOnto(Quaternion quatf, Vector offsetf) {
                     (SDWORD)(100 + 1000*mp + 0.4*mo);
     SDWORD tn, t0 = GetMilliseconds();
     double s = 0;
+    Quaternion dq = quatf.Times(quat0.Inverse());
     do {
         offset = (offset0.ScaledBy(1 - s)).Plus(offsetf.ScaledBy(s));
-        Quaternion quat = (quat0.ScaledBy(1 - s)).Plus(quatf.ScaledBy(s));
+        Quaternion quat = (dq.ToThe(s)).Times(quat0);
         quat = quat.WithMagnitude(1);
 
         projRight = quat.RotationU();

util.cpp

@@ -132,6 +132,28 @@ Vector Quaternion::Rotate(Vector p) {
             RotationN().ScaledBy(p.z));
 }
 
+Quaternion Quaternion::Inverse(void) {
+    Quaternion r;
+    r.w = w;
+    r.vx = -vx;
+    r.vy = -vy;
+    r.vz = -vz;
+    return r.WithMagnitude(1); // not that the normalize should be reqd
+}
+
+Quaternion Quaternion::ToThe(double p) {
+    Quaternion r;
+    Vector axis = Vector::MakeFrom(vx, vy, vz);
+    double theta = acos(w); // okay, since magnitude is 1, so -1 <= w <= 1
+    theta *= p;
+    r.w = cos(theta);
+    axis = axis.WithMagnitude(sin(theta));
+    r.vx = axis.x;
+    r.vy = axis.y;
+    r.vz = axis.z;
+    return r;
+}
+
 Quaternion Quaternion::Times(Quaternion b) {
     double sa = w, sb = b.w;
     Vector va = { vx, vy, vz };