Adaptive forward differencing for rendering curves and surfaces
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
A geometric characterization of parametric cubic curves
ACM Transactions on Graphics (TOG)
Rendering curves and surfaces with hybrid subdivision and forward differencing
ACM Transactions on Graphics (TOG)
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
A Tracking Algorithm for Implicitly Defined Curves
IEEE Computer Graphics and Applications
Elimination and Resultants - Part 1: Elimination and Bivariate Resultants
IEEE Computer Graphics and Applications
Comparison of interval methods for plotting algebraic curves
Computer Aided Geometric Design
OpenGL(R) Shading Language
Rasterizing complex polygons without tessellations
Graphical Models
Resolution independent curve rendering using programmable graphics hardware
ACM SIGGRAPH 2005 Papers
Resolution independent rendering of deformable vector objects using graphics hardware
ACM SIGGRAPH 2006 Sketches
Fast and simple hardware accelerated voxelizations using simplicial coverings
The Visual Computer: International Journal of Computer Graphics
GPU-accelerated path rendering
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
From theoretical graphic objects to real free-form solids
Information Sciences: an International Journal
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In this work, we describe a new algorithm for rendering polygons defined by cubic Bezier curve segments in current GPUs. Unlike other approaches, our algorithm has a simple preprocessing that does not require computing tessellations, and can be implemented in GPU as a geometry shader. The polygon is decomposed into a set of simplices which are individually rasterized into the stencil buffer to recreate the shape that is finally rendered in the frame buffer. Each simplex is rasterized using a fragment shader that evaluates the implicit equation of the Bezier curve to discard the pixels that fall outside it. The proposed method is simple, fast, robust and general, as it can handle curved polygons with holes, several components or self-intersections.