Hardware Supported Bump Mapping:
`
`A Step towards Higher Quality Real-Time Rendering
`
`l. Emst*, D. lackél“, H. Russeler*, O. Wittig*
`
`*German National Research Center for Information Technology,
`Institute for Computer Architecture and Software Technology (GMD FIRST)
`**University Rostock, Hansestadt Rostock Germany
`
`Abstract
`
`Today’s highland Gouraud renderers produce nicely textured scenes
`by mapping two-dimensional images onto modeled objects in real-
`time.
`
`We present a tenderer which textures surfaces in the normal sense of
`the word using bump textures to simulate wrinkled or dimpled color-
`ful surfaces. Using a simplified bump mapping method we first suc-
`ceeded in designing a real-time bump mapping renderer based on the
`high—quality Phong shading model.
`Applying several improvements to our former Phong shading hard-
`ware we are able to walk through perspectively correct bump mapped
`scenes illuminated by colored lightsources.
`This paper describes the main building blocks of the overall architec-
`ture, including reflectance cubes to support a local viewer, a Taylor-
`series based division to calculate homogeneous coordinates and our
`hardware adapted bump mapping method.
`
`Keywords: bump mapping. reflectance cube, normal vector interpo-
`lation, hardware division,
`local viewer, unh'mited colored light-
`sources, Phong shading, real-time rendering
`
`1. Introduction
`
`A contemporary "high-end" graphics workstations has a
`rendering performance of typically one million polygons
`per second in conjunction with hardware supported
`transparency, anti-aliasing, perspective texture mapping,
`image compositing, etc. In spite of the fact that great
`steps have been taken to improve the realistic display of
`very complex objects and scenes, many problems remain
`to be solved in order to achieve
`
`-
`
`image generation rate of complex scenes (>500.000
`polygons) of at least 30—50 frames per second
`
`- more photorealistic image generation by means of
`hardware supported “normal vector shading" as well
`
`as improved ,,anti-aliasing” or ,,bump mapping”.
`
`-
`
`linear scaleability of the rendering performance and
`an improvement of the cost—performance relationship.
`
`In the past decade, many attempts have been undertaken
`to make ,,normal vector shading” applicable for hard-
`ware implementations. M. Deering et a1. [6] presented a
`simulated VLSI-approach of a- semi vector shader
`(NVS) chip suitable for Phong shading [4]. Bishop and
`Weimar [3] suggested a method which approximates
`Phong’s normal interpolation and light reflection equa—
`tion by a Taylor series expansion. Bishop and Weimar’s
`fast Phoeg shading reduces the number of computation
`steps per pixel to only 5 additions and one memory
`access. Another alternative, suggested by U. Clausen [5],
`interpolates polar angles instead of normal vectors,
`which has the advantage that the normal vector unit
`length remains unchanged during the interpolation. Our
`normal-vector shading approach [11] is based on the
`approximation of the illumination model geometry by
`using the reflection map method. This shading tech—
`nique, which is used since 1989 in our VISA-systems
`(VISAzVISualization Accelerator), operates similar to
`the reflection vector shading hardware of Voorhies and
`Foran [13]. Instead of the single precalculated map of the
`VISA-shader, Voorhies and Foran propose a six~sided
`cube, which incorporates the specular spread function
`values. Similarly to the reflection map method, each face
`of the cube is indexed by an unnormalized reflection
`vector.
`
`An additional step towards photorealistic image genera-
`tion can be achieved by means of bump-mapping. Half
`of the work of hardware supported bump-mapping is
`done when using a normal vector shader instead of a
`gouraud shader. This paper is focus on the extension of
`our normal vector shading method for achieving a simple
`and efficient hardware bump—mapping support.
`
`First, we discuss the principle of hardware Phong—shad
`ing. In section 3 the extension of this shading technique
`to achieve bump-mapped surfaces is presented. Finally,
`the hardware implementation aspect of our bump-map-
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`ping method and some simulation results are discussed
`in more detail.
`
`the four neighboring cube elements reduces point sam-
`pling artifacts.
`
`2. Hardware Phong Shading
`
`Phong shading as proposed in [11], uses a planar reflec-
`tance map to “pick” the intensity.
`
`The “picking” of the reflectance map is done as follows:
`
`xn
`atan Zn
`
`J’n
`
`. a2 -— atan Zn}
`
`Considering the simplified geometry using parallel light
`and parallel viewer the amount of light reflected by an
`object’s surface is given by r = f((11, a2) .
`
`There are some disadvantages to our former approach
`using a reflectance map:
`
`' visible artifacts caused by point sampling the reflec-
`tance map;
`
`- visible distortions at the borders of the atan map
`(angle > 80 degrees);
`
`.
`
`illumination model allows parallel viewer only;
`
`~ costly computation for reflectance map if viewer
`changes.
`
`Solutions to reduce the size of the planar maps are given
`by for example in [12], [10]. To avoid distortions in the
`border area of the map, it is straightforward to use a
`hemi-cube over one polygon. This algorithm is com-
`monly used for radiosity methods and to approximate
`normal vector directions. Distortions which occur at the
`
`corners of the hemi—cube will be reduced by using an
`arctan map in the range of ~45 to 45 degrees, similar to
`the reflectance map approach. Bilinear interpolation of
`
`Elements contain
`spender value
`
`
`
`Despite the progress on planar or hemicube maps the
`restriction to parallel viewers could not be alleviated,
`One reason for this is that all progress is focused on the
`use of normal vectors to address cube faces. In [8], [13]
`
`it is proposed to use the reflection of the eye vector on
`the surface to address a six sided cube. Since the reflec-
`
`tion of the viewer is closely related to the specular com-
`ponent of the Phong shading algorithm, this method can
`also be applied to shading. Furthermore a six-sided cube
`contains all possible reflection vector directions around
`a fixed normal vector, the viewer can be local. As a con-
`
`sequence, this method allows for the View point to be
`changed without recomputation of the cube map.
`
`As indicated in [13] it is possible to calculate the reflec—
`tion vector R U without neutralization of the surface nor-
`mal NU and the eye vector by'multiplying both sides by
`the length of the unnormalized normal vector squared:
`
`RU = Z‘NU- (NUOE) —E- (NU-NU)
`
`(EQI)
`
`To calculate the diffuse component, another six sided
`cube map can be used which can be indexed by the
`unnormalized normal vector similar to the hemi cube
`
`approach. Calculating colors at the polygon vertices and
`bilinearly interpolating these colors over the polygon is
`not sufficient because highlights in the middle of a trian-
`gle cannot be generated. To reduce cube map space and
`calculation time methods proposed in [12], [10] are used.
`In Figure 1 the indexing of the cube ’5 faces is illustrated.
`
`Elements
`contain
`
`value
`
`
`
`specular cube
`
`diffuse cube
`
`Figure 1: Application of cube faces to calculate phong illumination
`
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`3. Bump mapping
`
`Bump mapping is an elegant technique to simulate wrin-
`kled or dimpled surfaces without the need to model sur-
`face properties geometrically.
`
`This is done by angular perturbing the surface normals
`according to information given in a two dimensional
`bump map.
`
`Since intensity is mainly a function of the surface nor—
`mal, the local reflection model produces local variations
`on a smooth surface dependent on the perturbation
`defined in the bump map.
`
`Bump mapping is important because it textures a surface
`in the normal sense of the word rather than modulating
`the color of flat surfaces.
`
`3.1. Classic Bump mapping
`
`Blinn [1] first developed a scheme that perturbs the nor-
`mal vector independently of the orientation and position
`of the surface. In the case of animations, otherwise it is
`
`obvious that the normal at a particular point must always
`receive the same rate of perturbation. Otherwise the
`bump map detail moves as the object moves. This is
`achieved by aligning the perturbation on a coordinate
`system based on local derivatives.
`
`If 0 (u, v) is a function representing position vectors of
`points 0 on the surface of an object, we first add a small
`increment, derived from the bump map B (u, v) to
`define 0’(u, v) :
`
`O’(u,v) = 0(u,v) +B(u,v)l%vn‘
`
`Because the displacement function B is small compared
`with its spatial extend by differentiating we get:
`
`N’(u,v) = Oux0v+Bu[I-M-><0v)
`B[0 xNj+BB(NXN)
`_
`“
`IN]
`a
`[N1
`
`+ v
`
`v
`
`2
`
`N
`
`
`
`(EQZI
`
`The last
`
`dropped.
`
`NxN
`
`term Bqu[‘—"§'] = 0
`
`and can be
`
`Note that the normal to a surface at a point is given by
`N 2: 0“ x 0v where O“ and 0V are the partial deriv—
`atives of the surface at point 0 lying in the tangent plane
`(see Figure 2).
`
`Figure 2:
`
`Tangent vectors 0" , 0v
`at a point on a sphere with
`
`normal vector N.
`
`From equation (HQ 2) it can be seen that implementing
`bump mapping in hardware is not possible without sim-
`plifying the calculation scheme.
`
`3.2. Hardware adapted Bump mapping
`
`Using Phong vertex normal interpolation, we already
`know the surface normal at a point. This surface normal
`N represents the orientation of the surface independent
`of the rotation about N.
`
`Our new tenderer VISA II will use a bump mapping
`scheme closely related to texture mapping.
`
`
`
`
`
`Vxtntautnonetuiogsuetl":
`
`
`
`clip coordinate system
`texture coordinate system
`Figure 3: Mapping from clip space to texture space
`
`65
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`The bump map describes the perturbation Au, Av of
`T .
`in texture space it, v, w
`
`normal [0, O, 1]
`
`The transformation matrix A carries out this mapping by
`projecting the local polygon coordinate system u’, v’, N
`on the texture coordinate system at, v, w.
`
`
`
`normals
`‘
`perpixclIIIXIIIII‘XITIT
`
`Figure 4: Effect of bump map on surface shape
`
`Figure 4 shows a precomputed bump map to simulate
`brick structures. Notice the u and v projections of line In
`and IV. The first line (shape) depicts surface orientations of
`the out along in, IV on the brick structure. The second line
`shows the displacement Au, Av . Positive Au, Av val-
`ues represent a displacement of the underlying pixel nor-
`mal
`in direction of u, v; negative values represent
`opposite directions. The third line shows the resulting sur-
`face shape and its perturbed surface normals. Notice the
`effect of the displacement between two brick stones to
`simulate the groove.
`
`Transformation of the bump map onto an object is done
`
`similar to texture mapping. By using homogenous coordi-
`nates the resulting address
`3’ 3 is the perspectively cor-
`rect pixel index on the bump map.
`
`To guarantee a perturbation in the desired direction a, v ,
`the object coordinate system must be transfonned such
`that the w -axis equals the surface normal vector direction
`N and the u - and v — coordinate axis are rotated about
`
`N according to the polygon mapping defined by the mod-
`eler.
`
`Figure 3 illustrates the mapping of the polygon
`
`[xv y], 21, W1] 7,
`
`{352, yr Z2, W2} T, [253, y3, z3, W3] T in the clip coordi-
`“1
`”1 T
`“'3 ‘7'
`W1 w}
`d.
`h
`.
`in t e texture coor mate sys-
`
`system 3:, y, z, to the edges
`nate
`v
`T
`u
`v
`T
`n
`3
`_2 .2
`__3_
`W2, W2
`, w3’ W3
`tem u, v, w.
`
`,
`
`per
`
`pixel
`
`normal
`
`To
`
`obtain
`
`the
`
`perturbed
`
`:r
`21’ n3 , Au,Av transformed by A isy’
`N’ = [11},
`
`T
`added to the surface normal N = [11,
`nynz]
`:
`
`n’ =nx+Au-A00+Av-A01
`
`n’ = ny—ernname/AMA11
`
`n =nz+Auu‘lZO-Hilv-A21
`
`The resulting normal is used to calculate the pixel color in
`the Phong illumination model described in the previous
`sections.
`
`4. Proposed Architecture
`
`The scan-converting procedure for triangles is described
`in detail in [11]. Given the triangle’s start coordinate with
`its start attributes and slope increments, the Scan Line Ini-
`tializer computes the relevant data at the start point of
`every new scanline, while the Pixei Calculator interpo—
`lates the coordinates and attributes within a scanline. This
`
`differs from the former design in the interpolation of an
`extended data set. In particular, we extend the interpolator
`to homogenous x, y, z, w space, which is necessary for
`achieving perspective texture mapping [9],
`texture,
`bump-coordinates (31,1?) eye vector [e e, eZr]
`
`After rasterization the obtained pixel fragment describes
`the position and orientation of small surface elementsin
`3D-space, the direction of reflection, the:- wtexture and
`bump coordinates
`
`Figure 5 shows a sketch of the proposed architecture.
`
`The non-shaded boxes will be discussed in more detail.
`
`The operation principle of the interpolation-units is pre-
`sented in [11]. To visit the pixels of adjacent triangles
`only once, the edge traverser was slightly modified [7].
`This is essential for color blending.
`
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`Input Parameter Set
`
`Selection of reflection map:
`
`lnterpoTtionmrpolarioT3xyz,w
`uv
`
`Noam!3;T-TVector .mlationof
`
`2
`y
`x
`color
`Figure 5: Overall blockdiagram of the rendering engine
`
`The bump engine perturbs the pixel normal by the corre-
`sponding bump map entry Au, Av. The bump map is
`aligned perpendicular to the surface normal. This is done
`by multiplying the bump map entries by A:
`
`
`
`Figure 6: Bump Engine
`
`—>
`-)
`N’: N+[Au,Av .A
`
`The reflectance cubes are addressed by the normal for the
`diffuse color component or by the reflected ray for the
`specular component. The address calculation unit for the
`reflected ray can be found, in [13]. The vector’s major axis
`determines the corresponding reflectance cube face.
`Indexing this map is done by dividing the vector’s minor
`axis values by the major axis value.
`
`z :-i-
`
`
`
`
`
`texturecolor
`
`
`
`BumpEngine.
`
`Reflectance cubes
`Addressing-unit
`
`materialcomponentKd,Ks,C01“light
`
`
`
`Ln,,ny, n]
`Address function:
`
`
`
`2|} , sign (nx, ny, n2)
`
`X— faces:
`
`"Z
`1 —, ——
`"II I";
`
`n
`
`n
`
`Y-faces: ——’-‘-1 —Z ,
`l1 1’5!
`n
`:1
`Z - faces: n—x
`
`y
`
`4.1. Division with on chip ROM
`
`Perspective correct texturing and calculating the intersec-
`tions of the normal and reflection vectors with the cube
`
`faces need one division per pixel. A common approach18
`to build the reciprocalw- followed by a multiplication.
`Convergence division algorithms normalize the divisor to
`apositive interval, typically 0,5 5 w < 1
`;positive num—
`bers are shifted up or down by a priority encoded shifter
`code. Negative numbers are first converted to signed pos-
`itive values (complement +1). The result ‘7, is corrected by
`the exponent of the normalization.
`
`In the following we focus on the computation of the recip-
`1
`.
`.
`.
`g, by Taylor—series approxrmauon [14] about
`roca]
`w = wk . After the normalization step, we can write:
`11-1
`1:
`
`w = 0,1w2w1...w
`
`m-I m
`w ...w
`
`W
`
`W}; = 0,1w2w3...wm_1wml...l.
`
`With Aw = w— wh so , one can develop
`
`1 .—
`W _
`
`Aw sz Aw3
`1
`a+—2'+“§‘+-—4'+....
`WI!
`Wh
`Wh
`
`For a reasonable hardware realization,
`
`the number of
`
`terms in the sum has to be small and the on-chip ROM
`implementation has to be memory efficient.
`
`Truncating after the third term of the sum and using B as
`the output of the look up table approximating 3;- , one can
`rewrite the above formula:
`"
`
`l
`17; = B+Bz-AW+B3-Aw2+error
`= B- (l+B~Aw' (l+B-Aw)) ,+error
`
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`The error is a function of the number of sum-terms t , the
`
`ative to the surface normal direction. To calculate the
`
`number of look-up-table entries m —1 and b the number
`of bits per word B . (Remember: m are the relevant bits
`
`of wt = 0,lw2w3..,wm_lwmll)
`
`Figure 7 shows the division by the homogenous factor
`w. With technology currently available, first simula-
`tions estimate an area of ca. 2.5me for this unit. The
`
`divisiOn of the vector’s major axis needs less accuracy.
`resalting in a smaller silicon area.
`normalized W
`
`
`
`Figure 7: Divider for llw
`
`correct perturbed normals for each per pixel. normal,
`recalculation of transformation matrix A for each pixel
`is necessary. Although the perturbation of pixel normals
`varying from the surface normal is not correct, it causes
`only a slight movement of the centroid of the highlight.
`
`In Figure 8, spherical interpolation of a per pixel normal
`(black) is shown. Given the shown lightsource and the
`viewer directions the centroid of the highlight
`lies
`exactly in the middle of the polygon. Applying linear
`interpolation (gray) the normal pointing exactly to the
`lightsource and the viewer is located slightly on the left
`causing the highlight to move to the left. In general this
`effect is not visible in animated scenes.
`
`9 L
`
`In
`
` a”
`
`'II
`.—
`centroid of highlight
`
`Figure 8: Spherical interpolation versus linear interpolaLiOn
`
`5. Results
`
`One limitation of the bump mapping method described
`above is that all normals on a polygon are perturbed rel-
`
`
`
`
`
`aft
`Figure 9: Mexican Hand Structure carved in tin plane
`
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`Another disadvantage caused by the calculation of A
`
`relative to the surface normal is shown in Figure 10:
`
`
`
`Figure 10: False illumination at edge of neighboring poly—
`gons.
`
`Simulating extreme curvature of adjacent polygon
`meshes by modeling vertex normals leads to machband
`effects at the edges. The vertex normal vl of mesh 1 is
`perturbed dependent on the surface normal (dashed nor-
`mal). The same rate of perturbation is applied to v2 of
`mesh 2 perpendicular to the surface normal of mesh 2
`(dashed gray normal). Assuming the vertex normal
`direction to be the perfect mirror direction, slight varia
`tions of vertex normals v1 and v2 generate different
`shading intensities. These shading intensity variations
`can be seen clearly along the edge revealing triangula-
`tion structures.
`
`to avoid
`Therefore the modeler’s responsibility is
`extreme curvature simulations or to use finer triangula-
`tion of these scene parts
`
`Figure 9 shows a bluish tin plane illuminated by a purple
`(upper left) and a white (front) lightsource. The plane is
`assembled out of two bump textured triangles. A Mexi-
`
`can head function is used to calculate the normal pertur—
`bation for a 40x40 bump map (see Figure 9 right).
`Applying the bump map to the plane repeatedly leads to
`the desired carving. The zoomed patch in the middle of
`Figure 9 clearly shows correct purple and white high~
`lights given by the illumination geometry.
`
`In Figure 11 the creation of complex images using con-
`ventional textures and bump textures is shown. In our
`example we rebuilt a small part of the “Berlin Wall"
`painting a graffiti texture (Figure 11 middle). To simu-
`late carving and rotting of the wall we created a grey-
`scale image which was converted to a bump map. Notice
`the writing “Berlin Haup(t)stadt" chiseled in the wall
`(see Figure 11 left (bump sketch) and right (resulting
`image». An animation of the “Berlin Wall" example
`scene generates the impression of moving sky trackers
`Over the rotten wall.
`
`6. Conclusions and Future Work
`
`We have designed and simulated a real time renderer
`supporting unique features like Phong shading and bump
`textures. With the presented renderer we are capable of
`generating animated scenes of higher quality then with
`conventional gouraud shading renderers.
`
`This technique could be improved further by:
`
`'
`
`techniques to simulate spherical interpolation of un-
`normalized normal vectors to avoid slight translations
`
`of highlights on polygons;
`
`- new hardware adapted methods to avoid artifacts
`
`caused by angle variations of neighboring polygons;
`
`‘ aitifact reduced MIP mapping for bump textures;
`
`.
`
`implementation of “living“ textures;
`
`
`
`Bump sketch
`
`Figure 11: Simulation of graffiti on rotten wall.
`
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`
`
`Hardware”, Siggraph Proceedings 1994, pp 163-166
`D. Wong, M. Flynn. “Fast Division Using Accurate Que-
`tient Approximations to Reduce the Number of Iterations”,
`IEEE TRANSACTION ON COMPUTERS. VOL.41, NO.
`8, pp. 981 - 995, August 1992
`
`' specification of a set of extensions for the OpenGL
`graphics language to support our unique graphic fea-
`tures.
`
`[14]
`
`Furthermore, it is desirable to switch between conven-
`
`tional texturing, bump texturing, reaction diffusion textur-
`ing and displacement mapping [2].
`
`’7. Acknowledgments
`
`We would like to thank the following people for their sug—
`gestions and contributions to this work: J. Duenow (scan-
`liner and parameter generation), L. Guangming (error
`analysis on division algorithms), T. Le Vin (Verilog simu~
`lation of arithmetic units, including silicon real estate esti~
`mation), and S. Budianto (Register Transfer Level
`Simulation). In addition, we would like to thank the many
`people who have commented on tlu's paper.
`
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`MEDIATEK, Ex. 1028, Page 8
`IPR2018-00102
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