Spaces 1D, 2D, and 3D Point Line Plan Points/Vectors A point p = (x,y,z) is also the vector p Vector Operation The Length of the vector v Normalization.

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Presentation transcript:

Spaces 1D, 2D, and 3D Point Line Plan

Points/Vectors A point p = (x,y,z) is also the vector p Vector Operation The Length of the vector v Normalization Dot product of u and v u v u+v

Vector Operation Cross Product Courtsy:Wikipedia

Lines Equation Parametric representation v

Plan Plan Normal Plan Equation

Point, Line, and Plan Point-line relation Inclusion, above/below Point-plan relation Inclusion, above/below Line-plan relation Intersection, inclusion, parallel, above/below Plan-plan relation Intersection, inclusion, parallel, above/below

Polyline and Polygon Vertices and Polyline Convex and Concave Polygons Simple and Complex Polygons Polygon Triangulation Inside and outside a Polygon Convex Hull