SIGGRAPH 2002 Notes

Stewart Dickson

Sunday, July 21 2002, 8:30AM

Course 2, "Advanced Global Illumination"

• The Rendering Equation -- a Fredholm integral equation of the second kind.
• Use Monte-Carlo (stochastic) numerical methods to solve
• BRDF -- Bi-Directional Radiance Distribution Function
• Ray Tracing is an "embarrassingly parallel" problem
• Spatial acceleration structure for rendering
• Load-balancing a non-uniform sample density distribution across the spatial domain.
• Free software test-bed for Global Illumination at:
  http://www.renderpark.be
  [expands to:]
  http://www.cs.kuleuven.ac.be/cwis/research/graphics/RENDERPARK/

Sunday, July 21 2002, 1:30PM

Course 4, "Multidimensional Visualization With Applications to Multivariate Problems"

• Visual data mining within a multi-dimensional data set
• Employ a parallel coordinate system, defined as follows:

In the Euclidean plane with xy-Cartesian coordinates, N copies of the real line labeled X₁, X₂, ... X_N are placed equidistant (e.g., 1 unit apart) and perpendicular to the x-axis. They are the axes of the parallel coordinate system for N-space all having the same positive orientation as the y-axis.

A point C with coordinates (c₁, c₂, ..., c_n) is represented by the complete polygonal line C (i.e., the lines of which only the local segments are usually shown) whose n vertices are at i + 1 c_i on the X_i-axis for i from 1 to N. [ ... ] In this way, a 1:1 correspondence between points in N-space and planar polygonal line with vertices on the parallel axes is established. The definition is deceptively simple and many people stop here without realizing the power of Parallel Coordinates which is really a whole METHODOLOGY.

• Lines in N-space correspond to points of intersection of many poly-lines in parallel coordinates.

Applications:

• Air traffic control (N-body problem of motion in 2 dimensions + time)
• Integrated circuit manufacturing yield
• Market economics.

"Parallax" software -- Inselberg.

• lasso-selection on a group of poly-lines in the parallel coordinate plane
• Seems to provide a great deal of understanding in how a select region of one of the parameters can localize a region of interest in the dataset.

• 1-80,000 points in 2-80 dimensions -- typical cases.
• high-dimensional LANDSAT raster image -- could have contained more than 80,000 pixels.
• General algorithm for classifying multi-dimensional data via a "nested hulls" method (of hypersurfaces in N-space) -- not presented explicitly, but intuitively observable.

Monday, July 22 2002, 8:30AM

Course 22, "Practical Parallel Rendering"

Examples:

• Interactive ray-tracer on a 32-processor (16Gb shared-memory) SGI Origin 3800
• Production render farm (Square Pictures, USA) ~100 dual-processor Pentium machines running Linux.

• Spatial domain data decomposition
• Decompose ray tracing algorithm into parallel "threads" or pipelines.

• Parallelizing compilers -- not good
• Multi-threading program design -- good
• Parallel threading run-time scheduler
• Cache traced ray paths between neighboring image pixels.

Clemson University Department of Computer Science is beginning to do parallel rendering using Chromium on a 240-node Linux cluster.

Monday, July 22 2002, 1:30PM

Course 25, "Using Tensor Diagrams to Solve Geometrical Problems"

• A graphical system of representing matrices and matrix operations
• A graphical algebra -- related to Clifford Algebra.

• Point-line (2-D) and point-plane (3-D) duality in homogeneous coordinates (projective space).
• Row and column vectors are 'mapped' to co-variant and contra-variant tensors.
• Diagram system represents transformationally invariant tensor properties.

• The Epsilon-Delta Identity has a very intuitive graphical presentation. Blinn used it several times to solve tensor problems.

• Line-surface, surface-surface intersections
• Converting between parametric and implicit forms of curve and surface descriptions
• Ideals
• Varieties
• Grobner Bases.

Course 35, "Super-Size It! Scaling up to Massive Virtual Worlds"