Add math/quatSlerp

Author: lexaknyazev

extensions/2.0/Khronos/KHR_interactivity/Specification.adoc

@@ -2110,6 +2110,56 @@ M = ((s_x, t_x, r_x),
 This operation implies that both input vectors are normalized. A `math/normalize` node could be added to handle non-normalized inputs.
 ====
 
+===== Quaternion Spherical Linear Interpolation
+
+[cols="1h,1,2"]
+|===
+| Operation | `math/quatSlerp` | Spherical linear interpolation operation
+.3+| Input value sockets
+d| `float4 a` | First quaternion
+d| `float4 b` | Second quaternion
+d| `float c` |  Unclamped interpolation coefficient
+| Output value sockets
+| `float4 value` | Interpolated value
+|===
+
+[CAUTION]
+====
+This node assumes that both input quaternions are unit.
+====
+
+The `value` output socket value is computed as follows:
+
+1. Let
+.. stem:[a_x], stem:[a_y], stem:[a_z], and stem:[a_w] be the components of stem:[a];
+.. stem:[b_x], stem:[b_y], stem:[b_z], and stem:[b_w] be the components of stem:[b].
+2. Let latexmath:[d = a_x \cdot b_x + a_y \cdot b_y + a_z \cdot b_z + a_w \cdot b_w].
+3. If latexmath:[d] is negative,
+.. set latexmath:[d] to latexmath:[-d];
+.. negate all components of the quaternion latexmath:[b].
+4. If latexmath:[d] is close to positive one within an implementation-defined threshold,
+.. let latexmath:[k_a = 1 - c], latexmath:[k_b = c].
+5. Else let:
+.. latexmath:[\omega = \arccos(d)];
+.. latexmath:[k_a = \frac{\sin(\omega \cdot (1 - c))}{\sin(\omega)}], latexmath:[k_b = \frac{\sin(\omega \cdot c)}{\sin(\omega)}].
+6. Set the components of the `value` output socket value using the following expressions:
++
+[latexmath]
++++++
+x = a_x \cdot k_a + b_x \cdot k_b \\
+y = a_y \cdot k_a + b_y \cdot k_b \\
+z = a_z \cdot k_a + b_z \cdot k_b \\
+w = a_w \cdot k_a + b_w \cdot k_b
++++++
+
+Since this operation is a shortcut for the combination of arithmetic and trigonometry operations, NaN and infinity values are propagated accordingly.
+
+[TIP]
+.Authoring Tip
+====
+This operation does not implicitly normalize the input quaternions. If needed, that step could be done explicitly by adding `math/normalize` nodes.
+====
+
 ==== Swizzle Nodes
 
 ===== Combine