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For Matt Parker's LED christmas tree project (https://www.youtube.com/watch?v=WuMRJf6B5Q4) I have created an animation showing the tree being cut into different conic sections (circle, ellipse, parabola and hyperbola). The animation was created in c#, using Rhino7 and Grasshopper. Each part of the animation is created with the equation of a 3D plane; as the position of the plane varies, each LED position is inserted into the plane equation to determine if that LED lies below or above the plane. In other words, this determines if the LED is turned on or off. To rotate the plane, a sine and cosine factor is added to the Y and X coefficients in the plane equation. This effectively rotates the plane around the Z-axis. The animation is best viewed perpendicular to the Y,Z plane, but can be enjoyed from any angle.

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Animation of conic sections on a 500 LED christmas tree

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