Figure 10.7: Parameter space T = [a; b] mapped to a curve c. The sample grid on T, as well as its corresponding mapped sample on c, has 15 points (not all labeled). The polyline l connecting the mapped sample approximates c.
Figure 10.8: A uniformly sampled parabola y = x 2.
Figure 10.14: (a) A double cone C showing two of the lines through the origin lying on it (b) A hyperbolic section of C by a non-radial plane p (c) Cross-sectional view of a non-radial plane p intersecting C.
Figure 10.15: Non-curves: (a) x 2 – y 2 = 0 (b) x 2 + y 2 = 0 (c) y = 0, if x is an integer, 1 otherwise (gaps in the blue line indicate missing points).
Figure 10.16: (a) A smooth curve (b) A non-smooth curve with a corner at P where the tangent changes direction abruptly.
Figure 10.26: Parametric mapping of a circular cylinder s.
Figure 10.27: Triangular mesh approximation of a circular cylinder. Upper: A uniform sample grid on the parameter rectangle and its corresponding mapped sample on the cylinder. Only a few points are labeled. Vertices of a triangle strip on the rectangle maps to those of a strip approximating a band of the cylinder. Lower: A map from a grid rectangle to a patch of the cylinder.
Figure 10.34: Computing parametric equations of a torus: (a) Profile circle c revolves along trajectory circle C (b) Sectional view of the left diagram along the plane containing the z-axis and OO’.
Figure 10.48: Generalized cones: (a) over a non-closed curve (b) over a closed curve (c) Right circular cone. Only the part between the two trajectories is drawn.
Figure 10.49: A generalized cylinder and a special case.
Figure 10.50: The nine non-degenerate quadric surfaces (from Wikimedia).
Figure 10.51: (a) Screenshot of hyperboloid1sheet.cpp (b) Edible hyperbolic paraboloids (c) Hyperboloid footbridge over Corporation Street in Manchester in England supported by its rulings (courtesy of Patrick Litherland).
Figure 10.71: Two bicubic Bezier patches and their control polyhedrons, one pair blue and one red. The patches meet smoothly along a shared boundary curve which, together with its control polygon, is black.
Figure 10.72: FreeGLUT library's version of the Utah teapot and Martin Newell's original porcelain Melitta model (from Wikimedia).