Lines, Curves and Surfaces in 3D

More documents

Recommendations

Info

Parametric Lines in 3D w p =(x, y, z) v 0 =(x 0 ,y 0 ,z 0 ) v tw v + tw CM0268 MATLAB DSP GRAPHICS 516 x = x 0 + ft y = y 0 + gt z = z 0 + ht 1 This is simply an extension of the vector form in 3D The line is normalised when f 2 + g 2 + h 2 = 1 ◭◭ ◮◮ ◭ ◮ Back Close
Perpendicular Distance from a Point to a Line in 3D For the parametric form, x = x 0 + ft y = y 0 + gt z = z 0 + ht CM0268 MATLAB DSP GRAPHICS 517 This builds on the 2D example we met earlier, line par point dist 2d. The 3D form is line par point dist 3d. dx = g * ( f * ( p(2) - y0 ) - g * ( p(1) - x0 ) ) ... + h * ( f * ( p(3) - z0 ) - h * ( p(1) - x0 ) ); dy = h * ( g * ( p(3) - z0 ) - h * ( p(2) - y0 ) ) ... - f * ( f * ( p(2) - y0 ) - g * ( p(1) - x0 ) ); 1 dz = - f * ( f * ( p(3) - z0 ) - h * ( p(1) - x0 ) ) ... - g * ( g * ( p(3) - z0 ) - h * ( p(2) - y0 ) ); dist = sqrt ( dx * dx + dy * dy + dz * dz ) ... / ( f * f + g * g + h * h ); The value of parameter, t, where the point intersects the line is given by: t = (f*( p(1) - x0) + g*(p(2) - y0) + h*(p(3) - z0)/( f * f + g * g + h*h); ◭◭ ◮◮ ◭ ◮ Back Close
Page 1: Lines, Curves and Surfaces in 3D Li
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 and 26: Parametric Surface: Cylinder (MATLA
Page 27 and 28: Piecewise Shape Models Polygons A p
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

Create successful ePaper yourself

Delete template?

Save as template?