On the numerical condition of polynomials in Berstein form
Computer Aided Geometric Design
Algorithms for polynomials in Bernstein form
Computer Aided Geometric Design
Scan line display of algebraic surfaces
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Computer Aided Geometric Design
Smooth piecewise quadric surfaces
Mathematical methods in computer aided geometric design
A polygonal approximation to direct scalar volume rendering
VVS '90 Proceedings of the 1990 workshop on Volume visualization
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
Jim Blinn's Corner: Notation, Notation, Notation
Jim Blinn's Corner: Notation, Notation, Notation
Microsoft DirectX 9 Programmable Graphics Pipeline
Microsoft DirectX 9 Programmable Graphics Pipeline
Resolution independent curve rendering using programmable graphics hardware
ACM SIGGRAPH 2005 Papers
How to solve a Quadratic Equation
IEEE Computer Graphics and Applications
ACM SIGGRAPH 2006 Papers
How to Solve a Cubic Equation, Part 2: The 11 Case
IEEE Computer Graphics and Applications
GPU-based rendering of sparse low-degree implicit surfaces
Proceedings of the 4th international conference on Computer graphics and interactive techniques in Australasia and Southeast Asia
Direct evaluation of NURBS curves and surfaces on the GPU
Proceedings of the 2007 ACM symposium on Solid and physical modeling
PCU: the programmable culling unit
ACM SIGGRAPH 2007 papers
An explicit quasi-interpolation scheme based on C 1 quartic splines on type-1 triangulations
Computer Aided Geometric Design
Interactive volume isosurface rendering using BT volumes
Proceedings of the 2008 symposium on Interactive 3D graphics and games
GPU conversion of quad meshes to smooth surfaces
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Technical strategies for massive model visualization
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Massive model visualization techniques: course notes
ACM SIGGRAPH 2008 classes
Computer Graphics Brazil: Scalable GPU rendering of CSG models
Computers and Graphics
Visualization of Industrial Structures with Implicit GPU Primitives
ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing
2D piecewise algebraic splines for implicit modeling
ACM Transactions on Graphics (TOG)
Optimized GPU evaluation of arbitrary degree NURBS curves and surfaces
Computer-Aided Design
Efficient substitutes for subdivision surfaces
ACM SIGGRAPH 2009 Courses
Adaptive quasi-interpolating quartic splines
Computing - Geometric Modelling, Dagstuhl 2008
High-Quality Rendering of Varying Isosurfaces with Cubic Trivariate C1-Continuous Splines
ISVC '09 Proceedings of the 5th International Symposium on Advances in Visual Computing: Part I
IEEE Transactions on Circuits and Systems for Video Technology
ACM SIGGRAPH ASIA 2009 Courses
Iterative methods for visualization of implicit surfaces on GPU
ISVC'07 Proceedings of the 3rd international conference on Advances in visual computing - Volume Part I
Extrusion and revolution mapping
ACM Transactions on Graphics (TOG)
GPU-accelerated 2D point cloud visualization using smooth splines for visual analytics applications
Proceedings of the 24th Spring Conference on Computer Graphics
Technical Section: Real-time ray casting of algebraic B-spline surfaces
Computers and Graphics
GPU-based parallel solver via the Kantorovich theorem for the nonlinear Bernstein polynomial systems
Computers & Mathematics with Applications
SMI 2012: Full A runtime cache for interactive procedural modeling
Computers and Graphics
Direct ray tracing of phong tessellation
EGSR'11 Proceedings of the Twenty-second Eurographics conference on Rendering
Design and novel uses of higher-dimensional rasterization
EGGH-HPG'12 Proceedings of the Fourth ACM SIGGRAPH / Eurographics conference on High-Performance Graphics
Wavelet-based multiresolution isosurface rendering
VG'10 Proceedings of the 8th IEEE/EG international conference on Volume Graphics
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
From theoretical graphic objects to real free-form solids
Information Sciences: an International Journal
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We consider the problem of real-time GPU rendering of algebraic surfaces defined by Bézier tetrahedra. These surfaces are rendered directly in terms of their polynomial representations, as opposed to a collection of approximating triangles, thereby eliminating tessellation artifacts and reducing memory usage. A key step in such algorithms is the computation of univariate polynomial coefficients at each pixel; real roots of this polynomial correspond to possibly visible points on the surface. Our approach leverages the strengths of GPU computation and is highly efficient. Furthermore, we compute these coefficients in Bernstein form to maximize the stability of root finding, and to provide shader instances with an early exit test based on the sign of these coefficients. Solving for roots is done using analytic techniques that map well to a SIMD architecture, but limits us to fourth order algebraic surfaces. The general framework could be extended to higher order with numerical root finding.