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Advanced Graphics Programming Using OpenGL by David Blythe, Tom McReynolds

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APPENDIX B

Equations

This appendix describes some important formulas and matrices referred to in the text.

B.1 3D Vectors

image

B.1.1 Spherical Coordinates

Given a point specified in Cartesian coordinates (x, y, z)T, the spherical coordinates (ρ, θ, φ) consisting of a length and two angles are

image

Given length ρ, azimuth angle φ, and elevation angle θ (assuming y is up) the Cartesian coordinates of the corresponding unit vector are

image

For unit vectors, ρ ...

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