Download presentation

Presentation is loading. Please wait.

Published byKeegan Maury Modified over 2 years ago

1
Computer Graphics Through OpenGL: From Theory to Experiments, Second Edition Chapter 10

2
Figure 10.1: One-dimensional objects.

3
Figure 10.2: Graphs of familiar plane curves (curves are fairly accurate sketches but not exact plots).

4
Figure 10.3: A couple of exotic curves.

5
Figure 10.4: More exotic curves.

6
Figure 10.5: A sphere and a plane intersect in a circle.

7
Figure 10.6: Helix.

8
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.

9
Figure 10.8: A uniformly sampled parabola y = x 2.

10
Figure 10.9: Screenshot of astroid.cpp.

11
Figure 10.10: (a) Curve with a repeating pattern (b) Ax head.

12
Figure 10.11: Supercircles |x| n + |y| n = 1, for n = 1/2, 1, 2, 4.

13
Figure 10.12: Points on a circle from a rational parametrization.

14
Figure 10.13: Conic sections.

15
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.

16
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).

17
Figure 10.16: (a) A smooth curve (b) A non-smooth curve with a corner at P where the tangent changes direction abruptly.

18
Figure 10.17: Tangent vectors to a circle.

19
Figure 10.18: Good and bad parametrizations.

20
Figure 10.19: Regular curves that share a tangent line at a common endpoint join to make one regular curve.

21
Figure 10.20: Various orders of continuity.

22
Figure 10.21: Camera moving along a path with a C 2 -discontinuity at the origin O.

23
Figure 10.22: (a) and (b) Non-simple planar polygons (c) and (d) Simple planar polygons (what we call polygons).

24
Figure 10.23: (a), (b) and (c) Meshes (d) and (e) Not meshes: parts around vertices V and W are not sheet-like (f) Your call.

25
Figure 10.24: Planar surfaces with colored boundary; the last one has two components. The black edges belong to approximating meshes.

26
Figure 10.25: Wooden chair.

27
Figure 10.26: Parametric mapping of a circular cylinder s.

28
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.

29
Figure 10.28: Screenshot of cylinder.cpp.

30
Figure 10.29: The composed mapping implemented in cylinder.cpp: first the parameter space is scaled, then mapped to the cylinder.

31
Figure 10.30: Screenshot of hemisphere.cpp.

32
Figure 10.31: Screenshot of helicalPipe.cpp.

33
Figure 10.32: Draw these by modifying cylinder.cpp.

34
Figure 10.33: Swept surfaces: trajectories dashed arrows, profiles solid black.

35
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’.

36
Figure 10.35: Screenshot of torus.cpp.

37
Figure 10.36: Screenshot of torusSweep.cpp.

38
Figure 10.37: (a) Part of a toroidal helix (b) Part of a toroidal helix pipe.

39
Figure 10.38: (a) The profile curve for a table on the xy-plane, with the z-coordinates, all 0, not written (b) A point on the profile curve after a rotation CW about the y-axis.

40
Figure 10.39: Screenshot of table.cpp.

41
Figure 10.40: (a) A cone and (b) a doubly-curled cone as swept surfaces.

42
Figure 10.41: Screenshot of doublyCurledCone.cpp.

43
Figure 10.42: Screenshot of extrudedHelix.cpp.

44
Figure 10.43: Stuff to draw.

45
Figure 10.44: Model these? You gotta be kidding!

46
Figure 10.45: A ruled surface showing several rulings and two defining trajectories.

47
Figure 10.46: Bilinear patch.

48
Figure 10.47: Screenshot of bilinearPatch.cpp.

49
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.

50
Figure 10.49: A generalized cylinder and a special case.

51
Figure 10.50: The nine non-degenerate quadric surfaces (from Wikimedia).

52
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).

53
Figure 10.52: GLU quadrics: (a) Sphere (b) Tapered cylinder (c) Annular disc (d) Partial annular disc.

54
Figure 10.53: Defining the GLU quadrics.

55
Figure 10.54: Regular polygons with number of sides indicated. The triangle shows its circumscribed circle.

56
Figure 10.55: The five regular polyhedra with the number of faces indicated.

57
Figure 10.56: Screenshot of tetrahedron.cpp.

58
Figure 10.57: The five regular polyhedra each containing its inscribed dual (the cube is labeled to help with Exercise 10.67).

59
Figure 10.58: Mapping a rectangle onto surfaces.

60
Figure 10.59: Patting gray a double torus.

61
Figure 10.60: Functions (u, v) → (f(u; v), g(u; v), h(u; v)) and their images.

62
Figure 10.61: Any neighborhood of P will consist of two intersecting fragments, which cannot lie in one coordinate patch.

63
Figure 10.62: (a) One coordinate patch wrapping almost all the way around a cylinder (b) A punctured square.

64
Figure 10.63: The non-zero linearly independent tangent vectors span the tangent plane p at P.

65
Figure 10.64: Various orders of surface continuity.

66
Figure 10.65: Screenshot of bezierCurves.cpp with six control points, showing both the Bezier curve and its control polygon.

67
Figure 10.66: Screenshot of bezier- CurveWithEvalCoord.cpp.

68
Figure 10.67: Two Bezier curves, one blue and one red, meet smoothly at an endpoint, as their control polygons meet smoothly (because v’, v and v’’ are collinear).

69
Figure 10.68: Screenshot of bezier- CurveTangent.cpp.

70
Figure 10.69: Screenshot of bezierSurface.cpp, showing both the surface mesh and its control polyhedron.

71
Figure 10.70: Screenshot of bezierCanoe.cpp.

72
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.

73
Figure 10.72: FreeGLUT library's version of the Utah teapot and Martin Newell's original porcelain Melitta model (from Wikimedia).

74
Figure 10.73: Screenshot of torpedo.cpp.

75
Figure 10.74: Bezier lady's shoe (courtesy of Pongpon Nilaphruek).

76
Figure 10.75: Aircraft and express train.

77
Figure 10.76: A coastline at increasing degrees of resolution: pairs of arrows indicate a blow-up.

78
Figure 10.77: Koch curves.

79
Figure 10.78: Screenshots from fractals.cpp: (a) Koch snowflake (b) Variant Koch snowflake (c) Tree.

80
Figure 10.79: The variant Koch curve and fractal tree.

81
Figure 10.80: A T-pipe is simulated by sticking one GLU cylinder into another.

82
Figure 10.81: Sheared? But, what about the other side?

Similar presentations

Presentation is loading. Please wait....

OK

The Geometry of Solids Section 10.1.

The Geometry of Solids Section 10.1.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on indian sea ports Ppt on mobile network layer Ppt on ac and dc generator Ppt on bond length definition Ppt on wind power generation Ppt on power grid failure drill Ppt on pricing policy Ppt on dhaka stock exchange Ppt on viruses and bacteria structure Download ppt on binomial theorem for class 11