2016
DOI: 10.1145/2897824.2925895
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Real-time polygonal-light shading with linearly transformed cosines

Abstract: In this paper, we show that applying a linear transformation---represented by a 3 x 3 matrix---to the direction vectors of a spherical distribution yields another spherical distribution, for which we derive a closed-form expression. With this idea, we can use any spherical distribution as a base shape to create a new family of spherical distributions with parametric roughness, elliptic anisotropy and skewness. If the original distribution has an analytic expression, normalization, integration over spherical po… Show more

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Cited by 71 publications
(57 citation statements)
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“…To solve the problem, Xu et al [XCM∗14] proposed a method to integrate a BRDF over a spherical triangle. Linearly Transformed Cosines (LTCs) [HDHN16] were introduced to analytically integrate a BRDF within a polygonal area. Spherical Pivot Transformed Distributions (SPTDs) [DHB17] were proposed to analytically integrates a BRDF within solid angles subtended by spheres.…”
Section: Related Workmentioning
confidence: 99%
See 1 more Smart Citation
“…To solve the problem, Xu et al [XCM∗14] proposed a method to integrate a BRDF over a spherical triangle. Linearly Transformed Cosines (LTCs) [HDHN16] were introduced to analytically integrate a BRDF within a polygonal area. Spherical Pivot Transformed Distributions (SPTDs) [DHB17] were proposed to analytically integrates a BRDF within solid angles subtended by spheres.…”
Section: Related Workmentioning
confidence: 99%
“…We use Spherical Pivot Transformed Distributions (SPTDs)[DHB17] to quickly compute an approximation of the integral. Other solutions, such as the Linear Transformed Consines (LTCs)[HDHN16] could give more accurate results, but with much more overhead.Light cluster sampling. For each shading point, once we have determined the light cut, i.e.…”
mentioning
confidence: 99%
“…An analytic convolution would have similar results as the virtual merge approach, but without the additional random decision. An approximate solution to this problem was given by Heitz et al [HDHN16] using cosine lobes.…”
Section: Johannes Jendersie Thorsten Grosch / Microfacet Model Regulmentioning
confidence: 99%
“…The area light is actually what we refer to as an LPAL. While real‐time rendering for scenes with area lights have been intensely studied [Arv95; Dro14; HDHN16; LDSM17], we employed the approach proposed by Heitz et al [HDHN16] because of its fast calculation and applicability to glossy surfaces. Following their method, we calculate the integration using the following formula:…”
Section: Indirect Illumination With Layered Polygonal Area Lightsmentioning
confidence: 99%