High-quality rendering of quartic spline surfaces on the GPU.

Area of Science:

• Computer Graphics
• Scientific Visualization
• Geometric Modeling

Background:

• Existing methods for rendering graph surfaces often rely on triangular meshes, leading to shading inaccuracies and artifacts.
• Tessellation introduces approximations that can compromise visual fidelity and level of detail.

Purpose of the Study:

• To develop a novel GPU-based algorithm for high-quality rendering of bivariate spline surfaces.
• To avoid the artifacts and inaccuracies associated with traditional triangular mesh tessellation.
• To enable direct computation of ray-surface intersections and surface normals on the GPU.

Main Methods:

• Utilized quartic smooth splines on triangulations instead of triangular meshes.
• Implemented a direct rendering approach computing ray-surface intersections numerically (solving quartic equations).
• Employed Bernstein-Bézier techniques for computing surface normals for Phong illumination on the GPU.

Main Results:

• Completely avoided inaccurate shading and artifacts common in triangular tessellated surfaces.
• Achieved automatic level of detail through per-fragment computations.
• Demonstrated highest quality visualizations, including texturing and advanced lighting, through hardware-based rendering.

Conclusions:

• The proposed GPU algorithm offers a superior method for rendering bivariate spline surfaces.
• Direct computation on the GPU eliminates tessellation artifacts, enhancing visual quality.
• The approach provides high-fidelity, artifact-free visualizations with automatic level of detail.