/*---------------------------------------------------------------------------*/
-void q_axisangle(const float *q, float *u, float *a)
+void q_as_axisangle(const float q[4], float u[3], float *a)
{
- *a = V_DEG(2.0f * facosf(q[0]));
+ *a = 2.0f * facosf(q[0]);
v_nrm(u, q + 1);
}
-void q_nrm(float *q, const float *r)
+void q_by_axisangle(float q[4], const float u[3], float a)
+{
+ float c = fcosf(a * 0.5f);
+ float s = fsinf(a * 0.5f);
+ float n[3];
+
+ v_nrm(n, u);
+
+ q[0] = c;
+ q[1] = n[0] * s;
+ q[2] = n[1] * s;
+ q[3] = n[2] * s;
+}
+
+void q_nrm(float q[4], const float r[4])
{
float d = q_len(r);
}
}
-void q_euler(float *v, const float *q)
+void q_mul(float q[4], const float a[4], const float b[4])
+{
+ q[0] = a[0] * b[0] - a[1] * b[1] - a[2] * b[2] - a[3] * b[3];
+ q[1] = a[0] * b[1] + a[1] * b[0] + a[2] * b[3] - a[3] * b[2];
+ q[2] = a[0] * b[2] - a[1] * b[3] + a[2] * b[0] + a[3] * b[1];
+ q[3] = a[0] * b[3] + a[1] * b[2] - a[2] * b[1] + a[3] * b[0];
+}
+
+void q_rot(float v[3], const float r[4], const float w[3])
+{
+ float a[4], b[4], c[4];
+
+ a[0] = 0.0f;
+ a[1] = w[0];
+ a[2] = w[1];
+ a[3] = w[2];
+
+ q_mul(b, r, a);
+
+ a[0] = r[0];
+ a[1] = -r[1];
+ a[2] = -r[2];
+ a[3] = -r[3];
+
+ q_mul(c, b, a);
+
+ v[0] = c[1];
+ v[1] = c[2];
+ v[2] = c[3];
+}
+
+void q_euler(float v[3], const float q[4])
{
float m11 = (2 * q[0] * q[0]) + (2 * q[1] * q[1]) - 1;
float m12 = (2 * q[1] * q[2]) + (2 * q[0] * q[3]);
v[2] = fatan2f(m23, m33);
}
+/*
+ * Spherical linear interpolation
+ */
+void q_slerp(float q[4], const float a[4], const float b[4], float t)
+{
+ float c, r, s, u, v;
+ int i = +1;
+
+ if (t <= 0.0f)
+ {
+ q_cpy(q, a);
+ return;
+ }
+
+ if (1.0f <= t)
+ {
+ q_cpy(q, b);
+ return;
+ }
+
+ /*
+ * a . b = |a||b| cos A
+ * |a| = |b| = 1
+ */
+
+ c = q_dot(a, b);
+
+ /* Ensure the shortest path. */
+
+ if (c < 0)
+ {
+ c = -c;
+ i = -1;
+ }
+
+ /* Fall back to normalized lerp for very similar orientations. */
+
+ if (1.0f - c < TINY)
+ {
+ u = 1.0f - t;
+ v = t;
+
+ i = 1;
+ }
+ else
+ {
+ r = facosf(c);
+ s = fsinf(r);
+ u = fsinf((1.0f - t) * r) / s;
+ v = fsinf((t) * r) / s * i;
+
+ i = 0;
+ }
+
+ q[0] = a[0] * u + b[0] * v;
+ q[1] = a[1] * u + b[1] * v;
+ q[2] = a[2] * u + b[2] * v;
+ q[3] = a[3] * u + b[3] * v;
+
+ if (i) q_nrm(q, q);
+}
+
/*---------------------------------------------------------------------------*/