queue-miscreant / approx-trig

Approximate trigonometry and quaternion rotation

approx-trigonometry

Some notes involving stereographic projections of the circle and sphere.

Files

quat.py

Notebook of symbolic manipulations involving quaternions.

sphere_tangent_proj.ggb

GeoGebra document demonstrating stereographic sphere and tangent plane at a point. Shows normal and tangent vectors at the point and demonstrates the "hairiness" of a sphere.

Approximate Trig/stereographic_trig.ggb

GeoGebra document demonstrating approximations for sine and cosine based on complex expression for a circle. Includes interpolation which improves accuracy to around 1%.

Approximate Trig/stereo_math.c

C program which tests speed of default implementations of sin and cos against the approximations derived in the above GeoGebra document.

Approximate Trig/stereo_complex.c

C program which tests speed of default implementation of cexp against the approximations derived in the above GeoGebra document.

Viewer/*

Sub-project: a 3D viewer written from scratch in Haskell using SDL. Uses the approximations derived above in conjunction with quaternions to create an image of a projection of 3D space.