angle_to was producing the angle from +x to the difference between a,b
which is unexpected. Instead, it should produce the smallest absolute
angle between the two vectors and be signed to indicate the direction of
rotation.
By using the old angle_to implementation and modifying equal() to print
out the failures, you can see the numbers that it was producing before
didn't make much sense:
right:angle_to(down) = 45.0
right:angle_to(left) = 0.0
right:angle_to(up) = -45.0
down:angle_to(right) = -135.0
down:angle_to(left) = -45.0
down:angle_to(up) = -90.0
left:angle_to(down) = 135.0
left:angle_to(up) = -135.0
up:angle_to(right) = 135.0
up:angle_to(down) = 90.0
up:angle_to(left) = 45.0
Now it produces numbers you'd expect:
right:angle_to(down) = -90.0
right:angle_to(left) = 180.0
right:angle_to(up) = 90.0
down:angle_to(right) = 90.0
down:angle_to(left) = -90.0
down:angle_to(up) = 180.0
left:angle_to(down) = 90.0
left:angle_to(up) = -90.0
up:angle_to(right) = -90.0
up:angle_to(down) = 180.0
up:angle_to(left) = 90.0
See also https://stackoverflow.com/questions/21483999/using-atan2-to-find-angle-between-two-vectors
Also added tests for angle_between.
- vec2 to_polar/from_cartesian tests were testing for equality rather than using an epsilon.
- bound2.contains had two tests that were plain wrong.
- While I'm fixing the bounds test, bound2.contains and bound3.contains probably ought to test their own min and max values for inclusion.
- The implementation of mat4.look_at appears to be wrong. The final column was being set to 0,0,0,1 which comparing against other implementations does not seem to be correct. My replacement code is modeled on the method used in mat4x4_look_at() in linmath.h in GLFW, which says it's a reimplementation on the method from gluLookAt(). With this change the test passes as originally written.
