Illumination for computer generated pictures
Summary (3 min read)
Methods of Object Modeling
- Image quality depends directly on the effectiveness of the shading algorithm, which in turn depends on the method of modeling the object.
- With these systems, exact information at each point of the surface can be obtained, and the result-ing computer generated pictures are most realistic.
- They have not been taken into consideration due to an increase in computation time to remove hidden surfaces and to perform shading computations.
- This type of representation has the advantage that it avoids the problem, posed by mathematically curved surface approaches, of solving higher order equations.
Shading with the Polyhedral Model
- When planar polygons are used to model an object, it is customary to shade the object by using the normal vectors to the polygons.
- The shading of each point on a polygon is then the product of a shading coefficient for the polygon and the cosine of the angle between the polygon normal and the direction of incident light.
2. Highlights created by specular reflection.
- Frame-to-frame discontinuities of shade in a computer generated film are illustrated in the following situation.
- A curved surface is approximated with planar facets.
- When this surface is in motion, all the facets which are perpendicular to the direction of the light take on a uniform shade.
- Thus the surface appears to change from one with highlights to one of uniform shade.
- Moreover, the position of these highlights is not steady from frame to frame as the object rotates.
Mach Band Effect
- Many of the shading problems associated with planar approximation of curved surfaces are the result of the discontinuities at polygon boundaries.
- One might expect that these problems could be avoided by reducing the size of the polygons.
- This would be undesirable, of course, since it would increase the number of polygons and hence would increase both the memory requirements for storing the model and the time for hidden surface removal.
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- Unfortunately, because of visual perception effects, the reduction of polygon size is not as beneficial as might be expected, The particular effect responsible is the Mach Band effect.
- Therefore unless the size of the displayed facets is shrunk to a resolution point, increasing the number of facets does not solve the problem.
- The subjective discontinuity of shade at the edges due to the Mach Band effect then destroys the smooth appearance of the curved surface.
- This new technique requires the computation of the normal to the displayed surface at each point.
Specular Reflection
- If the goal in shading a computer-synthesized image is to simulate a real physical object, then the shading model should in some way imitate real physical shading situations.
- I-Z LIGHT I LZ ignores both the position of the observer and the specular properties of the object.
- Even with the improvements introduced by Gouraud, which provide remarkably better shading, these properties are still ignored.
- The first step in accounting for the specular properties of objects and the position of the observer is to determine the normal to the surface at each point to be shaded, i.e. at each point where a picture element of the raster display projects onto the surface.
- It is evident from the preceding discussion, however, that their polyhedral model provides information about normals only at the vertices of polygons.
Computation of the Normal at a Point on the Surface
- The normal to the visible surface at a point located between two edges is the linear interpolation of the normals at the intersections of these two edges with a scan plane passing through the point under consideration.
- Note that the general surface normal is quadratically related to the vertex normal.
- From the approximated normal at a point, a shading function determines the shading value at that point.
The Shading Function Model
- In computer graphics, a shading function is defined as a function which yields the intensity value of each point on the body of an object from the characteristics of the light source, the object, and the position of the observer.
- The function W(i) and the power n express the specular reflection characteristics of a material.
- These numbers are empirically adjusted for the picture, and no physical justifications are made.
- In order to simplify the model, and thereby the computation of the terms cos(i) and cos(s) of formula (3), it is assumed that: 1. The light source is located at infinity; that is, the light rays are parallel.
- For a greater angle, this means that the light source is behind the front surface.
Conclusion
- The linear interpolation scheme used here to approximate the orientation of the normal does not guarantee a continuous first derivative of the shading function across an edge of a polygonal model.
- Also, an interesting fact discussed previously on Mach Band effect shows 317 that this effect is visible whenever there is a great change in the slope of the intensity distribution curve, even if the curve has a continuous first derivative.
- The Gouraud model needs one interpolator for the shading function.
- It must compute a new shading value for each raster unit, and hence must be very high speed to drive a real time display.
- In addition, since the results of the interpolation do not yield a unit vector, and since eqs. ( 6), (7) , and (8) require a unit normal vector, some extra hardware is necessary to "normalize" the outputs of the interpolators.
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Citations
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...BRDFs for a given surface can be obtained through physical modeling (Torrance and Sparrow 1967, Cook and Torrance 1982, Glassner 1995), heuristic modeling (Phong 1975), or through empirical observation, e....
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...Another model developed by Phong [40] represents the specular component of reflection as powers of the cosine of the angle between the perfect specular direction and the viewing direction....
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References
876Â citations
"Illumination for computer generated..." refers methods in this paper
...Several systems have been implemented to remove hidden parts for mathematically defined curved surfaces [1, 2, 3, 4, 5 ]. With these systems, exact information at...
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793Â citations
"Illumination for computer generated..." refers background in this paper
...(6), (7), and (8) require a unit normal vector, some extra hardware is necessary to "normalize" the outputs of the interpolators....
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...Z~ = cos(2i) = 2[cos(i)] 2 -- 1 = 2Z, 2 - 1, (6)...
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256Â citations
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...of Volume 18 the ACM Number 6 or "Bezier patches," Gouraud [ 11 ] developed an algorithm to shade curved surfaces....
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214Â citations
"Illumination for computer generated..." refers methods in this paper
...The two major advances in the development of fast hidden surface algorithms have been made by Watkins [9] and by Newell, Newell, and Sancha [10]....
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