Graphics II 91.547 Volume Rendering

1. Graphics II 91.547Volume Rendering Session 10

2. What do we mean by “volume rendering”?Conventional rendering: Bicubic Parametric Patches 2D Image Polygons 3D Structured Objects

3. What do we mean by “volume rendering”?The starting point: Scalar Field:

4. Volume Rendering:Options for presentation of the data Cutaway, or cross section Isosurface

5. What do we mean by “volume rendering”?What the samples mean: Voxel with samples at vertices. Voxel with sample at center.

6. What do we mean by “volume rendering”?The process: 2D Scalar Image Structured 3D Model 3D Scalar Field 3D Scalar Field

7. Data volume geometries Cartesian - (also known as a voxel grid) cubic data elements, axis aligned Preferred Regular - same as cartesian, except that the cells are rectangular, i.e. different sizes along different axes Most medical data Rectilinear - aligned to axes, but distance between cells along each axis can vary Structured or curvilinear non rectilinear, but cells are hexahedra rectangular warped to fill a volume or to fit around an object Often used in CFD Unstructured - no geometric constraints imposed

8. Outside Inside Early Volume Visualization TechniquesHerman & Liu 1979 Establish a threshold: Binary Partitioning of the volume: 2D Slice: “Boundary” Voxels are considered opaque cubes and rendered by standard lighting model.

9. Improving the blockiness of the image:The gradient operator

10. Approximating the gradient numerically:

11. Projecting from Contour Data:Pizer 1986 Polygon structure generated by “skimming”

12. Topological problem withPizer approach: branching structures

13. Outside Inside The “Marching Cubes” AlgorithmLorenson & Cline 1987

14. The “Marching Cubes” Algorithm

15. The “Marching Cubes” AlgorithmPossible Vertex States

16. The “Marching Cubes” AlgorithmGenerated contour

17. Generation of contour from subcontours

18. Generation of contour from subcontours:Disconnected regions

19. Marching Cubes AlgorithmPossible Polygon Arrangements

20. Marching Cubes AlgorithmPossible Polygon Arrangements

21. Marching Cubes Current cube Previously dealt with New vertex Direction of march

22. Weaknesses of Intermediate Structure Methods • Can impose a structure on the data which does not exist, per se. • Selection of a “constant” implies a binary decision on the existence of an intermediate surface that should be extracted and rendered • Could just be a gradual transition in density through the medium • Not feasible to visualize structures within structures • Does not handle objects that would intrinsically be transparent such as fluids, clouds

23. Volume rendering by ray castingBlinn 1982/Kajiya 1984 • Volume made up of small spherical particles that both scatter (reflect) and attenuate light • Parallel rays are cast from viewer into the volume. • At each point, the progressive attenuation due to the particle field is calculated • Light scattered in the eye direction from the light source(s) is calculated at each point • These values are integrated along the ray and a single brightness value at the eye is calculated

24. Scattering/Attenuation Model Light Source Eye Point R Density: Illumination: Light scattered along R in direction of eye from point at t:

25. Scattering/Attenuation Model Attenuation of light scattered from point t: Summing the intensity of light arriving at the eye along R from all of the elements:

26. Additive ReprojectionLevoy 1988 Image Plane R

27. Additive ReprojectionLevoy 1988 Determining the color of a voxel: Calculated using the Phong model, assuming that the normal is given by the gradient: Determining the opacity:

28. Additive ReprojectionLevoy 1988 kth voxel along R Transparency Term Opacity Term