Basic mathematics

Basic mathematics - Basic mathematics for geometric...

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Basic mathematics for geometric modeling
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Coordinate Reference Frames Cartesian Coordinate (2D) Polar coordinate x y (x, y) r θ
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x P Y x y r θ θ r x y P Use trigonometric, polar cartesian x = r cos θ , y = r sin θ Cartesian polar r = x 2 + y 2 , θ = tan -1 (y/x)
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3D cartesian coordinates x y z Right-handed 3D coordinate system z x y
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POINT The simplest of geometric object. No length, width or thickness. Location in space Defined by a set of numbers (coordinates) e.g P = (x, y) or P = (x, y, z) Vertex of 2D/ 3D figure
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distance and direction Does not have a fixed location in space Sometime called “displacement”. VECTOR
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VECTOR Can define a vector as the difference between two point positions. x y P Q x1 x2 y1 y2 V V = Q – P = (x2 – x1, y2 – y1) = (Vx, Vy) Also can be expressed as V = Vx i + Vy j Component form
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VECTOR : magnitude & direction Calculate magnitude using the Pythagoras theorem distance |V| = Vx 2 + Vy 2 Direction θ = tan -1 (Vy/Vx)
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Example 1 If P(3, 6) and Q(6, 10). Write vector V in component form. Answer
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This note was uploaded on 11/11/2011 for the course MATH 110 taught by Professor Staff during the Winter '08 term at BYU.

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Basic mathematics - Basic mathematics for geometric...

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