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Graphics II 91.547 Volume Rendering. Session 10. What do we mean by “volume rendering”? Conventional rendering:. Bicubic Parametric Patches. 2D Image. Polygons. 3D Structured Objects. What do we mean by “volume rendering”? The starting point:. Scalar Field:.
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Graphics II 91.547Volume Rendering Session 10
What do we mean by “volume rendering”?Conventional rendering: Bicubic Parametric Patches 2D Image Polygons 3D Structured Objects
What do we mean by “volume rendering”?The starting point: Scalar Field:
Volume Rendering:Options for presentation of the data Cutaway, or cross section Isosurface
What do we mean by “volume rendering”?What the samples mean: Voxel with samples at vertices. Voxel with sample at center.
What do we mean by “volume rendering”?The process: 2D Scalar Image Structured 3D Model 3D Scalar Field 3D Scalar Field
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
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.
Projecting from Contour Data:Pizer 1986 Polygon structure generated by “skimming”
Topological problem withPizer approach: branching structures
Outside Inside The “Marching Cubes” AlgorithmLorenson & Cline 1987
Marching Cubes Current cube Previously dealt with New vertex Direction of march
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
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
Scattering/Attenuation Model Light Source Eye Point R Density: Illumination: Light scattered along R in direction of eye from point at t:
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:
Additive ReprojectionLevoy 1988 Image Plane R
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:
Additive ReprojectionLevoy 1988 kth voxel along R Transparency Term Opacity Term