Comput. & Graphics, Vol. 21, No. 2, pp. 143-149, 1997 0 1997 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0097*493/97 s17.oo+o.oo PII: s0097-8493@6)00077-5 Graphics Hardware DESIGN Pi2INCIPLES OF HARDWARE-BASED PHONG SHADING AND BUMP-MAPPING K. BENNEBROEK’, I. ERNST’, H. RUSSELER2 and 0. WITTIG2+ ‘Department of Electrical Engineering, Networking Theory Group, University of Twente, Twente, The Netherlands *German National Research Center for Computer Science,Institute for Computer Architecture and Software Technology (GMD FIRST), Rudower Chaussee 5, 12489Berlin, Germany e-mail: [email protected] Abstract-The VISA+ hardwarearchitecture is the first of a new generationof graphicsaccelerators designedprimarily to renderbump-, texture-, environment- and environment-bump-mappedpolygons. This paperpresents examples of the maingraphical capabilities and discusses methods and simplifications usedto createhigh quality images.One of the key conceptsin the VISA + design,the useof reflectance cubes,is predestinedfor environmentmapping. In combinationwith bump-and texture-mapping it shows the strengthof our new architecture.Furthermore it justifiessome of the decisionsmade during simulationand developmentof the complexVISA+ architecture.0 1997Elsevier Science Ltd 1. INTBODUCI’ION interpolation approach can be important if diffuse Even the fastest high quality graphics workstations intensitiesare calculatedon an incremental basis. like the recently announcedInfiniteReality@ graphics The normal-vector shading approach of the acceleratorsare still basedon common texturing in GMD-FIRST is a reflection map method. This combination with Gouraud shading. With continu- shadingtechnique, implemented in the VISA system ously improving VLSI technologiesin combination [5l operatesin a similar way to the reflection-vector with CAD tools to support full custom chip design, shadinghardware of Voorhies and Foran [6], new graphic architectures must evolve. As an A logical extension of the normal vector inter- important step towards higher realism, real-time polation principle was to support bump-mapping[9]. Phong shading will be the next technology-pushin Bumps improve visual effects for low-end game, as computer graphics. well as high-end VR applications.A combination of Over the past few decades,many attempts have texture and bump-mapsfor extremely perspective been made, to make Phong shadingpracticable for and huge polygons reduces the total setup- and hardware implementation. Bishop and Weimar [1] transfer-timefor computer graphicsscenes. proposed a Taylor seriesapproximation for N.H. In this paper, the quality aspectsof homogeneous For a curvature lessthan 60”, forward differencinga versus non-homogeneousinterpolation for Phong quadratic polynomial fits quite well and reducesthe shading,bump-mapping, environment and environ- computational efforts to five additions per pixel. ment bump-mapping,will be discussed.Focusing on Deering [2] presenteda shaderthat interpolatesthe efficient division schemesfor perspective texturing normal and eye vectors. In both approaches, and cube-reflectancemapping, a proposedhardware exponentiation of the cosine function was done by architecture is discussedin more detail. table lookup, which leads to intolerable hardware size if a broad range of exponentsis to be supported. 2. BASIC FUNDAMENTALS Another method usesangular interpolation tech- 2.1. Phongshading niquesrather than vector interpolation. This has the Phong Illumination was introduced by Tong Bui advantagethat the vector length remainsunchanged Phong in 1975[7] as an empirical model to simulate during the interpolation. This way, normalization highlights on shiny surfaces.The model has been can be reduced to vectors at the vertices and acceptedas a very good approximation of physical calculatedin software. While an approach suggested highlights. Phong introduced a specular exponent, by U. Clausen [3] interpolates polar angles,Kuijk reflecting material properties,and modelledthe steep and Blake [4] expand this principle to angular falloff of the highlight as the cosine of the angle interpolation on great-circles.The resulting expres- between the eye-vector and reflected light-vector, sions,however, are rather complicated.The angular raisedto the specularexponent. For the implementa- tion of Phong Illumination on a per pixel basis,the normal vector has to be interpolated over a polygon. Normal vector interpolation shadersare therefore + Author for correspondence. called Phong shaders,in contrast to the commonly 143 144 K. Bennebroek,1. Ernst, H. Riisselerand 0. Wittig used Gouraud shadersthat interpolate color-values over the polygon (that may have been calculated using Phong Illumination!). Phong’s Illumination model consists of an ambient, a diffuse and a Note the additional BumpMorph parameterwhich specularcomponent, resulting in: is used to control the amplitude of the bump perturbation (length of P). Since this parameter is I=a+~(d(N.L)+s(R.E)“) (1) constant over the polygon, it can be included in the I matrix A. This way, Equation (3) can be simplifiedto: for all lightsourcesi in the scene,with a, d and s ambient, diffuse and specular column-vectors (R,G,B)= respectively to depict material and light- source properties. N depicts the surface normal To convert Pi from WC to ScreenSpacewe need vector, L the vector pointing from the point on the two multiplications for each of its componentsby i surface to the light source,R the mirrored vector of However, in Section 3.2 we explain why we have to L around N (reflected light vector) and E the calculate the reflected ray in WC instead of Screen- reflected eye vector. All vectors need to be normal- Space coordinates. Hence we must convert the ized. normal N from ScreenSpaceto WC too. This is done by three divisions (i). 2.2. Bump-mapping The resulting formula, which is implemented in In 1974, Blinn [8] developed a technique that our hardware, then becomes: enables a surface to appear wrinkled or dimpled N’=N+[A.P] (5) without the need to model this roughnessgeome- trically. Note that N is generated by interpolating the For this purpose,he defined a specialtexture map normalized edge normal vectors of the triangle. called bump-map B(u,v) containing displacementor Hence N is unnormalized inside the triangle which height values to perturb the local normal vector. The leads to small highlight shifts on the surface. This perturbed normal vector is given asN’= N+ D where artifact can not be recognizedbecause there are no D is the perturbation vector. To calculate D, he color differencesnear the edgesof adjacent triangles defined two other vectors lying in the tangent plane [91. of the surface given by N. Thesevectors are defined The alignment matrix A can be used not only to as A=NxO, and B=NxO,, where O(u,v) is a get the correct perturbation vector, but also to parametrized function representing the position rotate, stretch, mirror or shorten the perturbation vectors of point 0 on the surface. Then, the vectors for one triangle. componentsof D are given by A = B,A- B$, This way, he defined a bump-map function as a displace- ment but uses its derivatives at the point (u,v) to calculate D. D can be better expressedby 3.2. Hardware reflected ray Basedon the M*L model [IO], with homogeneous D = B,(N x 0,) - B,(N x 0,) (2) eye vector B = E and surfacenormal vector x = $ _ the homogeneous reflected ray in ScreenSpace where N/IN] is written as N. coordinatesleads to 3. SIMPLIFICATIONS 7l = [r,rYrz] 3.1. Hardware bump-mapping Hardware bump-mapping needs to be much = 2N(NE) - (NN)E simplerthan the classicalapproach [Equation (2)]. Instead of constructing a perturbation vector out of local derivatives which have to be defined, we already store it in the bump-map. Since we inter- (6) polate the normal over one triangle, we already have the tangent plane of the surface.Given the perturba- tion vector Pi = [AuAvlT in WC, we might construct = ~[r,r,r,] = 2--$N(NE) - -!-(NN)Ew3 the resulting normal vector as N= N+ P. To guarantee a perturbation in the direction O,, 0, of the tangent plane at point i, we have to align the = $(2N(NE) - (NN)E) = -$R texture coordinate systemu, v, w to the tangent plane system0,, 0,, N. This transformation is done by an Sincecalculating R in ScreenSpaceleads to higher alignment matrix A. Then the resulting normal precision multipliers and adders (extra bits for vector becomes N’= N+ A.P. Since we have a homogeneouscomponent), we convert E and N to homogeneousinterpolated normal vector, the equa- WC to reducethe overall gate-costsfor the Reflected tion expands to Ray Unit. Hardware-based Phong shading and bump mapping 145 3.3. Hardware Phong 3.3.2. Using DirectPhong@ (VISA+). The com- There are two ways to calculate the color mon problem for designersof hardware shadersis contribution of each lightsource. the exponentiation in the Phong formula. Gouraud 3.3.1. Using reflection maps (VISA). N and R are Shaderscalculate the intensitieson polygon-vertices used as an index into the diffuse and specular in software and interpolate these RGB values to reflection map respectively. producepixelvalues. The flaw in this approach is that Diffuse: no real, focused highlights can be achieved if the highlight lies within a polygon. This reduces the [wynz] + max { Inxll~yllnrl}, &+wynz) realismof the renderedscene. Attempts to implement Phong shading all use table lookups for the MapAddress = [cl,a,,] = exponentiation. This resultsin intolerable hardware sizes if different exponent