Prefiltering Two-Dimensional Polygons without Clipping

Lin, Zhouchen; Chen, Haitao; Shum, Heung-Yeung; Wang, Jian

doi:10.1080/2151237x.2005.10129189

Cited by 4 publications

(3 citation statements)

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“…We have carefully considered adopting an analytic solution to the antialiasing problem [Catmull 1978[Catmull , 1984Duff 1989;McCool 1995;Guenter and Tumblin 1996;Lin et al 2005;Schaefer 2011, 2013]. Unfortunately, under the general setting of a fullfledged real-time vector graphics rendering pipeline, this is not possible from both practical and theoretical standpoints.…”

Section: Related Work and Motivationmentioning

confidence: 99%

Massively-parallel vector graphics

et al. 2014

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We present a massively parallel vector graphics rendering pipeline that is divided into two components. The preprocessing component builds a novel adaptive acceleration data structure, the shortcut tree. Tree construction is efficient and parallel at the segment level, enabling dynamic vector graphics. The tree allows efficient random access to the color of individual samples, so the graphics can be warped for special effects. The rendering component processes all samples and pixels in parallel. It was optimized for wide antialiasing filters and a large number of samples per pixel to generate sharp, noise-free images. Our sample scheduler allows pixels with overlapping antialiasing filters to share samples. It groups together samples that can be computed with the same vector operations using little memory or bandwidth. The pipeline is feature-rich, supporting multiple layers of filled paths, each defined by curved outlines (with linear, rational quadratic, and integral cubic Bézier segments), clipped against other paths, and painted with semi-transparent colors, gradients, or textures. We demonstrate renderings of complex vector graphics in state-of-the-art quality and performance. Finally, we provide full source-code for our implementation as well as the input data used in the paper.

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Section: Related Work and Motivationmentioning

confidence: 99%

Massively-parallel vector graphics

et al. 2014

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“…Furthermore, Guenther and Tumblin [GT96] used quadrature prefiltering to further speed up the process, with analytic aliasing in one direction and sampling in the other. More recently, Lin et al [LCSW05] proposed an analytic evaluation approach for radially symmetric filters that is in spirit similar to this work, but they do not support linear functions nor negative filter lobes as needed for most practical applications [MN88], In addition, their implementation runs on the CPU while we describe a fully integrated GPU implementation. Note that while the filters in [MN88] were originally designed for reconstruction purposes, they are also used in sampling due to their favorable comparison to other variants.…”

Section: Related Workmentioning

confidence: 99%

Analytic Anti‐Aliasing of Linear Functions on Polytopes

Auzinger

Guthe

Jeschke

2012

Computer Graphics Forum

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This paper presents an analytic formulation for anti-aliased sampling of 2D polygons and 3D polyhedra. Our framework allows the exact evaluation of the convolution integral with a linear function defined on the polytopes. The filter is a spherically symmetric polynomial of any order, supporting approximations to refined variants such as the Mitchell-Netravali filter family. This enables high-quality rasterization of triangles and tetrahedra with linearly interpolated vertex values to regular and non-regular grids. A closed form solution of the convolution is presented and an efficient implementation on the GPU using DirectX and CUDA C is described.

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“…Each right triangle is parameterized by two values that index a lookup table to find the edge's contribution. A more recent algorithm [LCSW05b] removes the need of clipping polygons to pixels by taking the modulo of final pixel values. The method also has analytic solutions for polynomial filters, but cannot use filters with negative values because of the modulo operation.…”

Section: Introductionmentioning

confidence: 99%

Analytic Rasterization of Curves with Polynomial Filters

Manson

Schaefer

2013

Computer Graphics Forum

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Figure 1: Vector graphic art of butterflies represented by cubic curves, scaled by the golden ratio. The images were analytically rasterized using our method with a radial filter of radius three. AbstractWe present a method of analytically rasterizing shapes that have curved boundaries and linear color gradients using piecewise polynomial prefilters. By transforming the convolution of filters with the image from an integral over area into a boundary integral, we find closed-form expressions for rasterizing shapes. We show that a polynomial expression can be used to rasterize any combination of polynomial curves and filters. Our rasterizer also handles rational quadratic boundaries, which allows us to evaluate circles and ellipses. We apply our technique to rasterizing vector graphics and show that our derivation gives an efficient implementation as a scanline rasterizer.

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Prefiltering Two-Dimensional Polygons without Clipping

Cited by 4 publications

References 0 publications

Massively-parallel vector graphics

Massively-parallel vector graphics

Analytic Anti‐Aliasing of Linear Functions on Polytopes

Analytic Rasterization of Curves with Polynomial Filters

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