Implicit surface octrees for ray tracing point models
Proceedings of the Seventh Indian Conference on Computer Vision, Graphics and Image Processing
Higher order approximating normals and their impact on isosurface shading accuracy
Machine Graphics & Vision International Journal
Technical Section: Real-time ray casting of algebraic B-spline surfaces
Computers and Graphics
Short paper: view dependent rendering to simple parametric display surfaces
EGVE - JVRC'11 Proceedings of the 17th Eurographics conference on Virtual Environments & Third Joint Virtual Reality
Multi-scale space-variant FRep cellular structures
Computer-Aided Design
Accelerated visualization of dynamic molecular surfaces
EuroVis'10 Proceedings of the 12th Eurographics / IEEE - VGTC conference on Visualization
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Compact representation of geometry using a suitable procedural or mathematical model and a ray-tracing mode of rendering fit the programmable graphics processor units (GPUs) well. Several such representations including parametric and subdivision surfaces have been explored in recent research. The important and widely applicable category of the general implicit surface has received less attention. In this paper, we present a ray-tracing procedure to render general implicit surfaces efficiently on the GPU. Though only the fourth or lower order surfaces can be rendered using analytical roots, our adaptive marching points algorithm can ray trace arbitrary implicit surfaces without multiple roots, by sampling the ray at selected points till a root is found. Adapting the sampling step size based on a proximity measure and a horizon measure delivers high speed. The sign test can handle any surface without multiple roots. The Taylor test that uses ideas from interval analysis can ray trace many surfaces with complex roots. Overall, a simple algorithm that fits the SIMD architecture of the GPU results in high performance. We demonstrate the ray tracing of algebraic surfaces up to order 50 and nonalgebraic surfaces including a Blinn's blobby with 75 spheres at better than interactive frame rates.