Applied Geometry for Computer Graphics and CAD
Duncan Marsh - Collection Springer Undergraduate Mathematics Series (SUMS)
Résumé
Table of contents
Transformations of the Plane
Introduction
Translations
Scaling about the Origin
Reflections
Rotation about the Origin
Shears
Concatenation of Transformations
Applications
Instancing
Robotics
Homogeneous Coordinates and Transformations of the
Plane
Introduction
Homogeneous Coordinates
Points at Infinity
Visualization of the Projective Plane
Line Model of the Projective Plane
Spherical Model of the Projective Plane
Transformations in Homogeneous Coordinates
Translations
Scaling about the Origin
Rotation about the Origin
Concatenation of Transformations
Inverse Transformations
Rotation about an Arbitrary Point
Reflection in an Arbitrary Line
Applications
Instancing
Device Coordinate Transformation
Point and Line Geometry in Homogeneous
Coordinates
Homogeneous Coordinates and Transformations of Space
Homogeneous Coordinates
Transformations of Space
Translations
Scalings and Reflections
Rotations about the Coordinate Axes
Rotation about an Arbitrary Line
Reflection in an Arbitrary Plane
Applications
Computer-Aided Design
Orientation of a Rigid Body
Geometric Methods for Lines and Planes in Space
Projections and the Viewing Pipeline
Introduction
Projections of the Plane
Projections of 3-Dimensional Space
The Viewplane Coordinate Mapping
The Viewing Pipeline
Classification of Projections
Classification of Parallel Projections
Classification of Perspective Projections
Curves
Introduction
Curve Rendering
Parametric Curves
Arc Length and Reparametrization
Application: Numerical Controlled Machining and
Offsets
Conics
Classification of Conics
Conics in Standard Form
Intersections of a Conic with a Line
Parametrization of an Irreducible Conic
Converting from Parametric Form to
Implicit Form
Conics in Space
Applications of Conics
Bezier Curves I
Introduction
Bezier Curves of Low Degree
Linear Bezier Curves
Quadratic Bezier Curves
Cubic Bezier Curves
The Effect of Adjusting a Control Point
The General Bezier Curve
Properties of the Bernstein Polynomials
Convex Hulls
Properties of Bezier Curves
The de Casteljau Algorithm
Subdivision of a Bezier Curve
Applications
Rendering
Intersection of a Planar Bezier Curve and
a Line
Intersection of Two Bezier Curves
Bezier Curves II
Spatial Bezier Curves
Derivatives of Bezier Curves
Conversions Between Representations
Piecewise Bezier Curves
Rational Bezier Cuves
Properties of Rational Bezier Curves
de Casteljau Algorithm for Rational Curves
Projections of Rational Bezier Curves
Derivatives of Rational Bezier Curves
B-splines
Integral B-spline Curves
Properties of the B-spline Curve
B-spline Types
Application: Morphing or Soft Object Animation
The de Boor Algorithm
Derivatives of a B-spline
Non-Uniform Rational B-Splines (NURBS)
Projections of NURBS Curves
Derivatives of NURBS
Rational de Boor Algorithm
Knot Insertion
Surfaces
Introduction
Quadric Surfaces
Bezier and B-spline Surfaces
Properties of Bezier and B-spline Surfaces
Derivatives of Bezier and B-spline Surfaces
Surface Constructions
Extruded Surfaces
Ruled Surfaces
Translationally Swept Surfaces
Surfaces of Revolution
Surface Subdivision
Curve and Surface Curvatures
Curvature of a Plane Curve
Curvature and Torsion of a Space Curve
Curvature of Bezier Curves
Surface Curvatures
Solutions
References
Index
Caractéristiques techniques
| PAPIER | |
| Éditeur(s) | Springer |
| Auteur(s) | Duncan Marsh |
| Collection | Springer Undergraduate Mathematics Series (SUMS) |
| Parution | 10/08/1999 |
| Nb. de pages | 288 |
| Format | 17 x 23,5 |
| Poids | 500g |
| EAN13 | 9781852330804 |
| ISBN13 | 978-1-85233-080-4 |
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