Bezier Curves and Surfaces. Parametric curves and surface: SomeConcepts Bézier Cuvres: Concept and properties Bezier surfaces: Rectangular andTriangular Conversion of Rectangular and TriangularBezier surfaces
Bézier Curves and Surfaces • Parametric curves and surface: Some Concepts • Bézier Cuvres: Concept and properties • Bézier surfaces: Rectangular and Triangular • Conversion of Rectangular and Triangular Bézier surfaces
Parametric curves and surface. In Graphics, we usually design a scene andthen generate realistic image by usingrendering equation.It's necessary to introduce geometricmodeling for scene designHowtorepresent3Dshapes (models)incomputer?
Parametric curves and surface • In Graphics, we usually design a scene and then generate realistic image by using rendering equation. • It’s necessary to introduce geometric modeling for scene design. • How to represent 3D shapes (models) in computer?
History of Geometric Modeling·Surface Modeling（曲面造型）： In 1962, Pierre Bézier, an engineer ofFrenchRenault Car company, propose a new kind ofcurve representation, and finally developed asystem UNISURF for car surface design in 1972
History of Geometric Modeling • Surface Modeling : – In 1962, Pierre Bézier, an engineer of French Renault Car company, propose a new kind of curve representation, and finally developed a system UNISURF for car surface design in 1972
BeziercurvelPierre Bezier<BacktoLastPage><EullGlossarysDefinition:ABézier curve is a curved line orpath defined bymathematical equations.Itwas named after Pierre Bezier, a French mathematician and engineer who developed thismethod of computer drawing inthe late 1g6os while working forthe car manufacturerRenault.Mostgraphics softwareincludes a pentoolfordrawingpaths withBeziercurves.(Continuedbelow...)The most basic Bezier curve is made up of two end points and control handles attached toeachnode.Thecontrol handles definethe shape.ofthe curveon eithersideofthecommonnode.Drawing Bezier curves may seem baffling at first; it's something that requires somestudy and practice to grasp the geometry involved, But once mastered, Bezier curves are awonderful waytodraw!Pierre Bezier was bornSeptember 1, 1910 and died November 25,19g9 at the age of 89.In1985hewasrecognizedbyACMSIGGRAPHwithaStevenA.Coons'awardforhislifetimecontributiontocomputergraphics andinteractivetechniques.A Bezier curve with three nodes.The center node is selected and the control handles arevisible
• Pierre Etienne Bezier was born on September 1, 1910 in Paris. Son and grandson of engineers • He entered the Ecole Superieure d'Electricite and earnt a second degree in electrical engineering in 1931. In 1977, 46 years later, he received his DSc degree in mathematics from the University of Paris. • In 1933, aged 23, Bezier entered Renault and worked for this company for 42 years. • Bezier's academic career began in 1968 when he became Professor of Production Engineering at the Conservatoire National des Arts et Metiers. He held this position until 1979
·Solid Modeling（实体造型）：- In1973, Ian Braid of Cambridge Universitydeveloped a solid modeling system fordesigning engineering parts- Ian Braid presented in his dissertation'Designing with volumes", this work beingdemonstrated with the BUILD-1 system
• Solid Modeling : – In1973, Ian Braid of Cambridge University developed a solid modeling system for designing engineering parts. – Ian Braid presented in his dissertation “Designing with volumes”, this work being demonstrated with the BUILD-1 system