Solid Modeling Adam Finkelstein Princeton University COS 426, Spring 2003 3D Object Representations • Raw data o Point cloud o Range image o Polygon soup • Surfaces o Mesh o Subdivision o Parametric o Implicit • Solids o Voxels o BSP tree o CSG o Sweep • High-level structures o Scene graph o Skeleton o Application specific 3D Object Representations • Raw data o Point cloud o Range image o Polygon soup • Surfaces o Mesh o Subdivision o Parametric o Implicit • Solids o Voxels o BSP tree o CSG o Sweep • High-level structures o Scene graph o Skeleton o Application specific Implicit Surfaces • Points satisfying: F(x,y,z) = 0 Polygonal Model Implicit Model Bill Lorensen SIGGRAPH 99 Course #4 Notes Implicit Surfaces • Example: quadric o f(x,y,z)=ax 2 +by 2 +cz 2 +2dxy+2eyz+2fxz+2gx+2hy+2jz +k • Common quadric surfaces: o Sphere o Ellipsoid o Torus o Paraboloid o Hyperboloid H&B Figure 10.10 0 1 2 2 2 = − + + z y x r z r y r x Implicit Surfaces • Advantages: o Very concise o Guaranteed validity o Easy to test if point is on surface o Easy to intersect two surfaces • Disadvantages: o Hard to describe complex shapes o Hard to enumerate points on surface o Hard to draw
7
Embed
Solid Modeling CSG - Computer Science Department at Princeton
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
1
Solid Modeling
Adam FinkelsteinPrinceton University
COS 426, Spring 2003
3D Object Representations• Raw data
o Point cloudo Range imageo Polygon soup
• Surfaceso Mesho Subdivision o Parametrico Implicit
• Solidso Voxelso BSP treeo CSGo Sweep
• High-level structureso Scene grapho Skeletono Application specific
3D Object Representations• Raw data
o Point cloudo Range imageo Polygon soup
• Surfaceso Mesho Subdivision o Parametrico Implicit
• Solidso Voxelso BSP treeo CSGo Sweep
• High-level structureso Scene grapho Skeletono Application specific
CSG Boolean Operations• Create a new CSG node joining subtrees
o Uniono Intersectiono Difference
FvDFH Figure 12.27
CSG Display & Analysis• Ray casting
Circle Box
Union
Summary
Accurate No No Some SomeConcise No No No YesAffine invariant No No Yes YesEasy acquisition Some Some No SomeGuaranteed validity Yes Yes Yes NoEfficient boolean operations Yes Yes Yes YesEfficient display No No Yes No