Lines, Curves and Surfaces in 3D

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Parametric Surface: Sphere A sphere is represented in parametric form as x = x c +sin(u)∗sin(v) y = y c +cos(u)∗sin(v) z = z c +cos(v) CM0268 MATLAB DSP GRAPHICS 540 1 MATLAB code to produce a parametric sphere is at HyperSphere.m ◭◭ ◮◮ ◭ ◮ Back Close
Piecewise Shape Models Polygons A polygon is a 2D shape that is bounded by a closed path or circuit, composed of a finite sequence of straight line segments. CM0268 MATLAB DSP GRAPHICS 541 We can represent a polygon by a series of connected lines: P 3 (x 3 ,y 3 ) e 2 e 3 P 2 (x 2 ,y 2 ) P 6 (x 6 ,y 6 ) P 4 (x 4 ,y 4 ) e 1 e 6 e 7 P 1 (x 1 ,y 1 ) P 7 (x 7 ,y 7 ) e 5 e 4 P 5 (x 5 ,y 5 ) 1 ◭◭ ◮◮ ◭ ◮ Back Close
Page 1 and 2: Lines, Curves and Surfaces in 3D Li
Page 3 and 4: Perpendicular Distance from a Point
Page 5 and 6: Implicit Surfaces An implicit surfa
Page 7 and 8: Parametric Equation of a Plane (x 0
Page 9 and 10: Distance from a 3D point and a Plan
Page 11 and 12: Angle Between a Line and a Plane (c
Page 13 and 14: Angle Between Two Planes (MATLAB Co
Page 15 and 16: Intersection of a Line and Plane (M
Page 17 and 18: Intersection of Three Planes (MATLA
Page 19 and 20: Intersection of Two Planes (Cont.)
Page 21 and 22: Plane Through Three Points Just as
Page 23 and 24: Parametric Surfaces The general for
Page 25: Parametric Surface: Cylinder (MATLA
Page 29 and 30: 3D Objects: Boundary Representation
Page 31 and 32: Geometric Transformations Some Comm
Page 33 and 34: Applying Geometric Transformations
Page 35 and 36: Homogeneous Coordinates To work in
Page 37 and 38: Compound Geometric Transformations
Page 39 and 40: Least Squares Fitting We have alrea
Page 41 and 42: Least Squares Fit of a Line (Cont.)
Page 43 and 44: Least Squares Fit of a Line (MATLAB
Page 45 and 46: Least Squares Fit of a Plane (Cont.
Page 47 and 48: Simplifying a Least Squares Fit of
Page 49 and 50: Example Applications Visited • Ge

Lines, Curves and Surfaces in 3D

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