Interactive Curves and Surfaces
A Multimedia Tutorial on CAGD
- 1st Edition - August 1, 1996
- Latest edition
- Authors: Alyn Rockwood, Peter Chambers
- Language: English
The growing importance of animation and 3D design has caused computer-aided geometric design (CAGD) to be of interest to a wide audience of programmers and designers.This interacti… Read more
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Description
Description
The growing importance of animation and 3D design has caused computer-aided geometric design (CAGD) to be of interest to a wide audience of programmers and designers.
This interactive software/book tutorial teaches fundamental CAGD concepts and discusses the growing number of applications in such areas as geological modeling, molecular modeling, commercial advertising, and animation. Using interactive examples and animations to illustrate the mathematical concepts, this hands-on multimedia tutorial enables users without a substantial mathematical background to quickly gain intuition about CAGD.
Interactive Curves and Surfaces guides you in* Learning the uses of CAGD as it is applied in computer graphics and engineering.* Creating curved lines and surfaces using Bezier curves, B-Splines, and parametric surface patches.* Understanding the mathematical tools behind the generation of these objects, and the development of computer-based CAGD algorithms.* Experimenting with powerful interactive test benches to explore the behavior and characteristics of the most popular CAGD curves.Application oriented readers will find this animated tutorial presentation more accessible than the standard formal texts on the subject.
Table of contents
Table of contents
Interactive Curves and Surfaces: A Multimedia Tutorial on CAGDby Alyn Rockwood and Peter Chambers
- PrefaceInstalling the SoftwareHow to Use the Electronic BookTopic 1: Introduction to CAGD
- What CAGD Is All AboutA Design Challenge: The Need for CAGDCAGD: From Points to TeapotsA CAGD Favorite: The Bezier CurveThree-Dimensional Control Polygons for Surfaces (Control Meshes)Three-Dimensional Wireframe ModelThree-Dimensional Shaded ObjectThe History of CAGDWhat Has Been Accomplished in This Topic
- The Mathematics of CAGDParametric FormsThe Parametric CurveSingle-ValuedInfinite SlopeTransformation ProblemsDefining the Parametric CurveThe Parametric Circle, t = 0.16 (approximately 57 degrees)The Parametric Circle, t = 0.33 (approximately 118 degrees)The Parametric Circle, t = 0.67 (approximately 241 degrees)Bezier Tangent DemonstrationThe Parametric SurfaceParametric DerivativesThe Hodograph of the Bezier CurveThe Vector Construction of the HodographContinuityExercisesLinear InterpolationExercisesLinear Interpolation between Two Points, t = 0.125Linear Interpolation between Two Points, t = 0.25Linear Interpolation between Two Points, t = 0.5Basis FunctionsWhat Has Been Accomplished in This Topic
- Introduction to the Bezier CurveThe Cubic Bezier CurveMathematical Properties of the Bezier CurveThe Quadratic Bezier CurveBezier Curves of General DegreeBinomial CoefficientsBernstein FunctionsThe Cubic Bernstein Basis FunctionsExerciseCharacteristics of the Bezier CurveEndpoint InterpolationTangent ConditionsConvex HullAffine InvarianceVariation DiminishingLinear PrecisionThe de Casteljau AlgorithmDe Casteljau's Algorithm for a Degree 2 Bezier CurveStep OneStep TwoStep ThreeStep FourString ArtA Demonstration of de Casteljau's AlgorithmStep OneStep TwoStep ThreeStep FourSubdivision of a Bezier CurveBefore the SubdivisionAfter the SubdivisionUses of SubdivisionDesign RefinementClipping a Curve to a BoundaryA Cubic Bezier Curve before SubdivisionA Cubic Bezier Curve after SubdivisionHigher Degree Bezier CurvesA Degree 8 Bezier CurveThe Derivative of the Bezier CurveThe Hodograph of the Bezier Curve with Its Control PolygonContinuity of the Bezier CurveDegree Elevation of the Bezier CurveA Cubic Bezier Curve Elevated to DegreeWhat Has Been Accomplished in This Topic
- Background to InterpolationComparison of the Bernstein and Lagrange Basis FunctionsEndpoint InterpolationTangent ConditionsAffine InvarianceConvex HullVariation DiminishingLinear PrecisionExerciseEvaluation of the Lagrange CurveHermite InterpolationExercisesOther Interpolation FormsWhat Has Been Accomplished in This Topic
- IntroductionBlossom BasicsNotationPoint Ordering Is Not SignificantExerciseSummary of Blossoming form Linear InterpolationThe History of BlossomsThe Formal Definition of BlossomsExamples of BlossomsExercisesThe Power of the Blossom FormSubdivision of the Bezier Curve Using BlossomsEvaluating a Blossom from Bezier Control PointsThe EvalBlossom AlgorithmEvalBlossomProg: A General Blossom AlgorithmIllustration of the Cubic BlossomWhat Has Been Accomplished in This Topic
- IntroductionThe de Boor AlgorithmSummary of B-Splines in Blossom FormEvalBlossomProgExercisesPeriodic B-SplinesNonuniform B-SplinesBasis FunctionsGeneral Basis FunctionsExperiment with the B-Spline CurveKnot InsertionWhat Has Been Accomplished in This Topic
- IntroductionThe Two-Dimensional Rational Bezier CurveFinding the Conic SectionsThe General Rational Bezier CurveRational B-Spline CurvesWhat Has Been Accomplished in This Topic
- Introduction to SurfacesProperties of the Bezier Surface PatchEndpoint InterpolationTangent ConditionsConvex HullAffine InvarianceVariation DiminishingPlanar PrecisionEvaluation of the Bezier Surface PatchUniform B-Spline SurfacesWhat Has Been Accomplished in This Topic
- IntroductionEvaluating Surface Characteristics: Reflection MapsG0 ContinuityG1 ContinuityG2 ContinuityEvaluating Surface Characteristics: Hedgehog DisplayG0 ContinuityG1 ContinuityG2 ContinuityFaceting: The Display of Complex SurfacesThe Utah Teapot: Texturing and Bump MappingThe Utah Teapot Rendered by ContouringSimple Display and Illumination of a Turbine BladeImage GalleryAutomobile Front EndSki BootMachine GearBicycle WheelStill LifeWhat Has Been Accomplished in This Topic
- Other CurvesOther SurfacesNonrectangular PatchesTriangular PatchesOther Surface DefinitionsImplicit and Parametric SurfacesWhat Has Been Accomplished in This Topic
Product details
Product details
- Edition: 1
- Latest edition
- Published: August 22, 1996
- Language: English