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A note from the author

As a practicing aerospace engineer, I frequently encounter problems that require math skills I don’t have and must learn. Early in my career I adopted the habit of writing down the solutions to these problems in a personal Engineering Notebook. If a problem took more than a trivial amount of time to research, and was general enough that I might run into it again some day, into the notebook it went.

The articles on this website are based on those engineering notes. They represent practical, battle-tested solutions to real-world problems. Technology changes, but math is eternal. I hope these papers save you some time.

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			Converting between Earth-Centered, Earth Fixed and Geodetic Coordinates How to convert from Geodetic coordinates (latitude, longitude and height above ellipsoid) to Earth-Centered, Earth-Fixed coordinates, and back again. Includes example code.
			Rotating Points in Two-Dimensions The efficient way to rotate points around an arbitrary center on a two-dimensional Cartesian plane.
			Rotations in Three-Dimensions: Euler Angles and Rotation Matrices Describes a commonly used set of Tait-Bryan Euler angles, and shows how to convert from Euler angles to a rotation matrix and back.
			Rotation Quaternions, and How to Use Them An introduction to rotation quaternions. Shows how to perform rotations, and how to convert between quaternions, rotation matrices, axis-angle, and Euler angles.
			Solving 2x2, 3x3, 4x4 and 5x5 Systems of Linear Equations on a Computer A general solution to systems of linear equations of up to 5 equations and 5 unknowns, using Cramer's Method.
			Interpolation Methods for interpolating one-dimensional signals, images, and 2D graphics. Based on Catmull-Rom cubic spline.

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