parallel computation of the minimum separation distance of bezier curves and surfaces
DESCRIPTION
Parallel Computation of the Minimum Separation Distance of Bezier Curves and Surfaces. Lauren Bissett, [email protected] Nicholas Woodfield, [email protected] REU Biogrid, Summer 2009 University of Connecticut Storrs, CT 06269. Presentation Summary. - PowerPoint PPT PresentationTRANSCRIPT
Parallel Computation of the Minimum Separation Distance of Bezier Curves
and Surfaces
Lauren Bissett, [email protected]
Nicholas Woodfield, [email protected]
REU Biogrid, Summer 2009University of ConnecticutStorrs, CT 06269
Presentation Summary
Background Overview CUDA Bezier Curves Bezier Surfaces Benefits/Future work
Background
Animation relies on continuous movement between frames to give the illusion of motion.
When an unexpected change occurs between frames, this is known as temporal aliasing.
Background
One method of dealing with temporal aliasing is detecting self-intersections in geometric objects.
If self-intersections are unnoticed by an animator, it could lead to the animation looking 'off'.
A scientist looking at a visual of a complicated molecule likewise could not determine if there are self-intersections.
Background
One method to detect self-intersections is finding a geometric object's minimum separation distance.
The minimum separation distance is the smallest doubly normal segment between any two points on the object.
A segment is doubly normal if both its endpoints are normal to the curve/surface.
Background
The algorithm for finding the minimum separation distance is time-consuming and not practical for use.
Therefore NVIDIA's CUDA parallel programming langauge will be used to implement the algorithms so that they run fast enough for practical use.
CUDA
CUDA was developed by NVIDIA for parallel programming on the GPU.
Allows the launch of thousands of parallel threads of execution.
Unlike most GPU programming, CUDA development is relatively easy, because it extends C (with additional bindings for C++ and Fortran).
It also allows for general programming, no prior knowledge of graphics required
CUDA Memory Model Threads – basic
element of execution, has own register and local memory
Blocks – composed of threads, has own shared memory
Grid – composed of blocks, contains global, constant and texture memory
Our Machine
The machine used for this research used a QuadroFX 5800 GPU running Windows Vista.
512 threads per block 32 registers per thread
Minimum Separation Distance
To find the minimum separation distance, there are three major steps:
Generate candidate double normal segments Newton's method Find segment of minimum segment length
Finding Candidate Segments
The method of finding potential double normal segments is simple but time-consuming.
For a given sample size (n), take n sample points and pair with all other points in the sample.
Then check if each pair is creates a double normal segment.
Finding Candidate Segments
Newton's Method
The initial estimates are run on Newton's method until they converge.
When finished, the double normal segment is compared to determine if it is of smallest length.
Bezier Curves
Curve case implemented first It's simple – only two parametric values – (s,t) – to
worry about
Bezier Curve Kernel Organization Used a 1-Dim grid composed of 1-Dim blocks Blocks divided into groups, one for each curve Threads responsible for one s parametric value on
only one curve Each thread tests its sample points vs all other points
on it's parent curve and all other curves If the candidate segment passes the double normal
test, we run newton's method on it Each thread ultimately returns the shortest segment
from its search
Bezier Curve Kernel Organization
What problems can arise? Sample size > maximum thread allowance Register usage Must ensure consistency among multiple blocks
E.g. If we used a thread's built in index value,
and we used 2 blocks per curve, each block
would then only test values between 0 and .5! This required equations to calculate which thread
belonged to whom
Bezier Curve Kernel Results
Double normals returned in a 2D array Rows are blocks Columns are threads in a block
Launched a second kernel to collapse the array into a 1-Dim array the size of the # of blocks
Iterated over those segments, and found the shortest which is our minimum separation distance
Results
8x to 200x speedup
n e1 e2 C code CUDA code
512 0.4 0.4 28s 154.76ms
512 0.2 0.2 26s 154ms
200 0.4 0.4 4.3s 46.6ms
10 0.4 0.4 15ms 1.81ms
Bezier Surfaces
Next we moved onto surfaces – bicubic bezier meshes.
Bezier Surfaces
Surfaces are just an extension of curves, but with two parametric values – u and v.
Each thread in the kernel handles a u,v pair. It then checks against all other u,v pairs on the surface.
Blocks were extended into 2 Dimensions, to represent the unit square.
Bezier Surfaces
Similar to curves, the thread determines if the segment is doubly normal, and if necessary, discards an old one of greater length if it finds a short one.
And again, Newton's method is run on each doubly normal segment.
Finally, a similar search through results to find the minimum separation distance
Bezier Surfaces
The thread results are again searched for the smallest segment, which is the minimum separation distance.
Results?
The mesh algorithm was largely completed in the last few days
Curve case, although simple, took two weeks of tweaking until the code was sastifactory
Mesh case still needs some tweaking Still confident we'll observe similar results to the
curve case However, we do not have comparable C code to
compare results
Benefits/Future work
How does this tie into bio-grid? Nature of the problem:
Self-intersections in molecule simulations are of interest
Leveraging the GPU for general programming 'Supercomputing for the masses' Tremendous speedups for low costs Useful for when supercomputing power is not
present nor available
Future work: Finish the mesh case!
Questions and Answers
Any Questions?
Images
CUDA Memory Model, Dr. Dobbs Supercomputing for the Masses: http://www.ddj.com/architect/208401741?pgno=3
Double normal segments & surfaces double normals, Ed Moore's Ph.D. Thesis
Newton's method: http://en.wikipedia.org/wiki/Newton%27s_method
Bezier surface w/control points: http://www.cs.cf.ac.uk/Ralph/graphicspics/bez.GIF