## Tracing Ray Differentials (1999)

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Citations: | 63 - 0 self |

### BibTeX

@MISC{Igehy99tracingray,

author = {Homan Igehy},

title = {Tracing Ray Differentials},

year = {1999}

}

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### Abstract

Antialiasing of ray traced images is typically performed by supersampling the image plane. While this type of filtering works well for many algorithms, it is much more efficient to perform filtering locally on a surface for algorithms such as texture mapping. In order to perform this type of filtering, one must not only trace the ray passing through the pixel, but also have some approximation of the distance to neighboring rays hitting the surface (i.e., a ray's footprint). In this paper, we present a fast, simple, robust scheme for tracking such a quantity based on ray differentials, derivatives of the ray with respect to the image plane. CR Categories and Subject Descriptors: I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism -- color, shading, shadowing, and texture; raytracing. 1 INTRODUCTION Ray tracing [18] is an image generation technique that is able to accurately model many phenomena which are difficult or impossible to produce with a traditional graphics pip...

### Citations

575 |
An improved illumination model for shaded display
- Whitted
- 1980
(Show Context)
Citation Context ... image plane. CR Categories and Subject Descriptors: I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism – color, shading, shadowing, and texture; raytracing. 1 INTRODUCTION Ray tracing =-=[18]-=- is an image generation technique that is able to accurately model many phenomena which are difficult or impossible to produce with a traditional graphics pipeline. As with any image synthesis algorit... |

379 |
Distributed ray tracing
- Cook, Porter, et al.
- 1984
(Show Context)
Citation Context ...to aliasing, and antialiasing is typically performed by tracing rays at multiple sub-pixel offsets on the image plane (e.g., [12, 18]). By stochastically point sampling each of many variables per ray =-=[6]-=-, one may filter over multiple phenomena simultaneously. For some algorithms, however, it is much more efficient to filter over a more local domain. For example, in texture mapping, a texture will oft... |

357 |
Principles of Optics
- Born, Wolf
- 1964
(Show Context)
Citation Context ...he simpler field of elementary differential calculus is that our formulation is easier to understand, and extending the technique to handle different phenomena is straightforward. Paraxial ray theory =-=[4]-=- is an approximation technique originally developed for lens design, and its application to ray tracing is known as pencil tracing [16]. In pencil tracing, paraxial rays to an axial ray are parameteri... |

317 |
An introduction to ray tracing
- Glassner
- 1989
(Show Context)
Citation Context ...ially offset ray intersects the surface in the tangent plane of the intersection point. 3.1.2 Reflection Given a ray that has been transferred onto a surface by (9), the equation for a reflection ray =-=[7]-=- is given by: P′ = P D′ = D − 2( D ⋅ N)N For a ray differential, reflection is given by: where: ∂P′ = ∂P ∂x ∂x ∂ ( ) ( ⋅ ) D ⋅ N ∂N D N ∂D′ = ∂D − 2⎡ + ∂x ∂x ⎢⎣ ∂x ( D⋅N) ∂ ∂x ∂x N⎤ ⎥⎦ (13) (14) = ∂D ... |

153 |
Generating antialiased images at low sampling densities
- MITCHELL
- 1987
(Show Context)
Citation Context ...hics pipeline. As with any image synthesis algorithm, ray tracing is prone to aliasing, and antialiasing is typically performed by tracing rays at multiple sub-pixel offsets on the image plane (e.g., =-=[12, 18]-=-). By stochastically point sampling each of many variables per ray [6], one may filter over multiple phenomena simultaneously. For some algorithms, however, it is much more efficient to filter over a ... |

140 |
RealityEngine graphics
- Akeley
- 1993
(Show Context)
Citation Context ...the utility of ray differentials in performing texture filtering. 2 RELATED WORK Several algorithms have been developed for estimating a texture filtering kernel in polygon rendering pipelines (e.g., =-=[1, 10]-=-). Similar algorithms have been used in ray tracers that calculate the projection of texture coordinates onto the image plane [8], butsuch a projection is only valid for eye rays. This technique can ... |

116 |
Lectures on classical differential geometry
- Struik
- 1950
(Show Context)
Citation Context ...s (18) (19) The formulae derived for reflection and refraction of ray differentials in Sections 3.1.2 and 3.1.3 depend on the derivative of the unit normal with respect to x. In differential geometry =-=[17]-=-, the shape operator (S) is defined as the negative derivative of a unit normal with respect to a direction tangent to the surface. This operator completely describes a differentially small area on a ... |

103 | Ray tracing with cones
- Amanatides
- 1984
(Show Context)
Citation Context ...ed over an area on a surface’s illumination map based on the density of rays [5]. § Dull reflections may be modeled by filtering textures over a kernel which extends beyond the ray’s actual footprint =-=[2]-=-. In this paper, we introduce a novel approach for quickly and robustly tracking an approximation to a ray’s footprint based on ray differentials. Ray tracing can be viewed as the evaluation of the po... |

56 | Illumination from curved reflectors
- Mitchell, Hanrahan
- 1992
(Show Context)
Citation Context ...f the ray density when a ray is intersected against an object. § When ray tracing caustics, the intensity attributed to a sampled light ray depends upon the convergence or divergence of the wavefront =-=[13]-=-. Similarly, in illumination mapping, the flux carried by a ray from a light source must be deposited over an area on a surface’s illumination map based on the density of rays [5]. § Dull reflections ... |

36 | Bmrt: A global illumination implementation of the renderman standard
- Gritz, Hahn
- 1996
(Show Context)
Citation Context ...g a texture filtering kernel in polygon rendering pipelines (e.g., [1, 10]). Similar algorithms have been used in ray tracers that calculate the projection of texture coordinates onto the image plane =-=[8]-=-, butsuch a projection is only valid for eye rays. This technique can be extended to reflected and refracted rays by computing the total distance traveled, but such an approximation is invalid becaus... |

33 |
Texram: A Smart Memory for Texturing
- Schilling, Knittel, et al.
- 1996
(Show Context)
Citation Context ...oordinates. if the parallelogram defined by (25) is asymmetric. Anisotropic filtering techniques take into account both the orientation and the amount of anisotropy in the footprint. A typical method =-=[3, 15]-=- is to define a rotated rectangle based on the longer of the two axes of the parallelogram, use the rectangle’s minor axis to choose a mip map level, and average bilinear samples taken along the major... |

25 | Adaptive splatting for specular to diffuse light transport
- Collins, S
- 1994
(Show Context)
Citation Context ...ce of the wavefront [13]. Similarly, in illumination mapping, the flux carried by a ray from a light source must be deposited over an area on a surface’s illumination map based on the density of rays =-=[5]-=-. § Dull reflections may be modeled by filtering textures over a kernel which extends beyond the ray’s actual footprint [2]. In this paper, we introduce a novel approach for quickly and robustly track... |

7 | Texture Mapping Polygons in Perspective
- Heckbert
- 1983
(Show Context)
Citation Context ...eline is straightforward because primitives are drawn in raster order, and homan@graphics.stanford.edu the transformation between texture space and image space is described by a linear projective map =-=[10]-=-. In a ray tracer, however, the primitives are accessed according to a pixel’s ray tree, and the transformation between texture space and image space is non-linear (reflection and refraction can make ... |

7 |
Using wavefront tracing for visualization and optimization of progressive lenses
- Loos, Slusallek, et al.
- 1998
(Show Context)
Citation Context ...nd it has been used to calculate caustic intensities resulting from illumination off of curved surfaces [13]. Wavefronts have also been used to calculate the focusing characteristics of the human eye =-=[11]-=-. Although highly interrelated, the main difference between wavefronts and our method of ray differentials is that our method tracks the directional properties of a differentially small distance while... |

6 |
Pyramidal Parametrics. Computer Graphics (SIGGRAPH 83 Proceedings
- Williams
- 1983
(Show Context)
Citation Context ...he rays for a neighboring pixel when the ray hit the texture map (i.e., a ray’s footprint), then we could efficiently filter the texture by using a fast, memory coherent algorithm such as mip mapping =-=[19]-=-. Tracing such a quantity in a polygon rendering pipeline is straightforward because primitives are drawn in raster order, and homan@graphics.stanford.edu the transformation between texture space and ... |

5 |
High-quality rendering using the talisman architecture
- Barkans
- 1997
(Show Context)
Citation Context ...oordinates. if the parallelogram defined by (25) is asymmetric. Anisotropic filtering techniques take into account both the orientation and the amount of anisotropy in the footprint. A typical method =-=[3, 15]-=- is to define a rotated rectangle based on the longer of the two axes of the parallelogram, use the rectangle’s minor axis to choose a mip map level, and average bilinear samples taken along the major... |

4 |
Decorating Implicit Surfaces
- Pederson
- 1995
(Show Context)
Citation Context ...rdinates of a surface depend on the texture parameterization of the surface. Such a parameterization is straightforward for parametric surfaces, and algorithms exist to parameterize implicit surfaces =-=[14]-=-. In general, the texture coordinates of a surface may be expressed as a function of the intersection point: ( P) T = f (23) We can differentiate with respect to x to get a function that is dependent ... |

1 |
Die reelle optische Abbildun g
- Gullstrand
- 1906
(Show Context)
Citation Context ...be used for algorithms such as anisotropic texture filtering. In addition, extending the technique to support surfaces other than planar polygons and spheres in not straightforward. Wavefront tracing =-=[9]-=- is a method in which the properties of a differentially small area of a ray’s wavefront surface is tracked, and it has been used to calculate caustic intensities resulting from illumination off of cu... |