graphics ii 91 547 volume rendering l.
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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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what do we mean by volume rendering conventional rendering
What do we mean by “volume rendering”?Conventional rendering:

Bicubic Parametric Patches

2D Image


3D Structured Objects

what do we mean by volume rendering what the samples mean
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
What do we mean by “volume rendering”?The process:

2D Scalar Image

Structured 3D


3D Scalar Field

3D Scalar Field

data volume geometries
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

early volume visualization techniques herman liu 1979



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
Projecting from Contour Data:Pizer 1986

Polygon structure generated by “skimming”

marching cubes
Marching Cubes

Current cube

Previously dealt with

New vertex

Direction of march

weaknesses of intermediate structure methods
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 casting blinn 1982 kajiya 1984
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
Scattering/Attenuation Model

Light Source

Eye Point




Light scattered along R in direction of eye from point at t:

scattering attenuation model25
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 reprojection levoy 198827
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 reprojection levoy 198828
Additive ReprojectionLevoy 1988

kth voxel along R