CPSC 424 Rational Curves Syllabus - Ugrad.cs.ubc.ca

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Rational Curves Other properties: • Convex hull • Curve interpolates start and endpoint (rational Bézier only) • De Casteljau, de Boor and other algorithms now have to be performed in homogeneous coordinates! © Alla Sheffer & Wolfgang Heidrich OpenGL void gluNurbsCurve( GLUnurbsObj *nobj, GLint nknots, GLfloat *knot, GLint stride, GLfloat *ctlarray, GLint order, GLenum type ) nobj - pointer to object created by gluNewNurbsRenderer nknots - number of knots knot – knot vector stride - “width” = dimension ctlarray - array of control points. order - degree+1 type - enum of types © Alla Sheffer & Wolfgang Heidrich 4
OpenGL - example GLfloat knots[8] = { 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0 }; gluBeginCurve(nurb); gluNurbsCurve(nurb, 8, knots, 3, &ctlpoints[0][0], 4, GL_MAP1_VERTEX_3); gluEndCurve(nurb); © Alla Sheffer & Wolfgang Heidrich Subdivision Curves Represent smooth curve by approximating polyline At the limit = curve Each iteration • Add new points (~double) • Approximating - Move old points • Interpolating – Keep old points © Alla Sheffer & Wolfgang Heidrich 5
Page 1 and 2: CPSC 424 Rational Curves © Alla Sh
Page 3: Rational Curves Definition: • A r
Page 7 and 8: Corner Cutting © Alla Sheffer & Wo
Page 9 and 10: Corner Cutting © Alla Sheffer & Wo
Page 11 and 12: Cubic B-Spline (corner cutting) 3/4
Page 13 and 14: The 4-point scheme © Alla Sheffer

CPSC 424 Rational Curves Syllabus - Ugrad.cs.ubc.ca

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