Add cross and dot product functions

Author: jonathanhogg

docs/builtins.md

@@ -71,9 +71,16 @@ the length of the longest vector; short arguments will repeat, so
 generalises to n-vectors, returning a vector the length of the longest of
 *x*, *y* and *z*, and repeating items from any of the vectors as necessary.
 
+`cross(` *x*, *y* `)`
+: Compute the cross product of two 3-vectors.
+
 `cos(` *x* `)`
 : Return cosine of *x* (with *x* expressed in *turns*).
 
+`dot(` *x*, *y* `)`
+: Compute the dot product of two n-vectors. This is the equivalent of
+`sum(x * y)`.
+
 `exp(` *x* `)`
 : Return $e$ raised to the power of *x*.
 

src/flitter/language/functions.pyx

@@ -804,6 +804,14 @@ def hypot(*args):
     return ys
 
 
+def cross(Vector xs not None, Vector ys not None):
+    return xs.cross(ys)
+
+
+def dot(Vector xs not None, Vector ys not None):
+    return xs.dot(ys)
+
+
 def normalize(Vector xs not None):
     return xs.normalize()
 
@@ -815,9 +823,9 @@ def quaternion(Vector axis not None, Vector angle not None):
 
 
 def qmul(Vector a not None, Vector b not None):
-    if a.numbers == NULL or a.length != 4 or b.numbers == NULL or b.length != 4:
+    if a.numbers == NULL or a.length != 4 or b.numbers == NULL or b.length not in (3, 4):
         return null_
-    return Quaternion._coerce(a) @ Quaternion._coerce(b)
+    return Quaternion._coerce(a) @ (Quaternion._coerce(b) if b.length == 4 else b)
 
 
 def qbetween(Vector a not None, Vector b not None):
@@ -1046,7 +1054,9 @@ STATIC_FUNCTIONS = {
     'colortemp': Vector(colortemp),
     'cos': Vector(cosv),
     'count': Vector(count),
+    'cross': Vector(cross),
     'cubic': Vector(cubic),
+    'dot': Vector(dot),
     'exp': Vector(expv),
     'floor': Vector(floorv),
     'fract': Vector(fract),

tests/test_functions.py

@@ -10,7 +10,7 @@
 from flitter.language.functions import (uniform, normal, beta,
                                         lenv, sumv, accumulate, minv, maxv, minindex, maxindex, mapv, clamp, zipv, count,
                                         roundv, absv, expv, sqrtv, logv, log2v, log10v, ceilv, floorv, fract,
-                                        cosv, acosv, sinv, asinv, tanv, hypot, normalize, polar, angle, length,
+                                        cosv, acosv, sinv, asinv, tanv, hypot, normalize, polar, angle, length, cross, dot,
                                         quaternion, qmul, qbetween, slerp,
                                         split, ordv, chrv,
                                         colortemp, oklab, oklch)
@@ -537,6 +537,21 @@ def test_normalize(self):
         self.assertEqual(normalize(Vector([3, 4])), Vector([3, 4]) / Vector(5))
         self.assertEqual(normalize(Vector([3, 4, 5])), Vector([3, 4, 5]) / Vector(math.sqrt(50)))
 
+    def test_cross(self):
+        self.assertEqual(cross(null, null), null)
+        self.assertEqual(cross(Vector([3, 4]), Vector([3, 4, 5])), null)
+        self.assertEqual(cross(Vector([3, 4, 5]), Vector([3, 4])), null)
+        self.assertEqual(cross(Vector([3, 4, 5]), Vector([3, 4, 5])), Vector([0, 0, 0]))
+        self.assertEqual(cross(Vector([1, 0, 0]), Vector([0, 1, 0])), Vector([0, 0, 1]))
+        self.assertEqual(cross(Vector([0, 1, 0]), Vector([0, 0, 1])), Vector([1, 0, 0]))
+        self.assertEqual(cross(Vector([0, 0, 1]), Vector([1, 0, 0])), Vector([0, 1, 0]))
+
+    def test_dot(self):
+        self.assertEqual(dot(null, null), null)
+        self.assertEqual(dot(Vector([3, 4]), Vector([3, 4, 5])), Vector(3*3 + 4*4 + 3*5))
+        self.assertEqual(dot(Vector([3, 4, 5]), Vector([3, 4])), Vector(3*3 + 4*4 + 5*3))
+        self.assertEqual(dot(Vector([3, 4, 5]), Vector([5, 4, 3])), Vector(3*5 + 4*4 + 5*3))
+
     def test_polar(self):
         self.assertEqual(polar(null), null)
         self.assertEqual(polar(Vector('hello')), null)