BSNS102 Study Guide - Final Guide: Cartesian Coordinate System, Cross Product, Barycentric Coordinate System
28 Jan 2021
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The basic idea is to realize that we can translate the triangle without affecting the area. In this case, we will shift the triangle vertically by subtracting y3 from each of the y coordinates. (you can achieve the same simplifications using only algebraic manipulations. ) Computing the area of a 2d triangle from the coordinates of the vertices. In 3d we can use the cross product to compute the area of a triangle. Recall from section 5. 11. 2 that the magnitude of the cross product of two vectors a and b is equal to the area of the parallelo- gram formed on two sides by a and b. Since the area of a triangle is half the area of the enclosing parallelogram, we have a simple way to calculate the area of the triangle. Given two edge vectors from the triangle, e1 and e2, the area of the triangle is given by:
