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Shading methods
This document discusses different methods for shading 3D graphics objects rendered as polygons, including flat shading (assigning a single color to each polygon), Gouraud shading (interpolating colors across polygon surfaces), Phong shading (interpolating normal vectors and applying lighting models at each surface point), and fast Phong shading (approximating Phong shading calculations for improved performance). Gouraud shading improves on flat shading by removing intensity discontinuities, while Phong shading produces more realistic highlights but requires more computation.
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Shading involves implementing illumination models on graphics objects. These models define how light interacts with surfaces, identifying two light sources: emitting and reflecting.
Ambient light is uniformly distributed, creating diffuse illumination. Different shading methods include Constant-intensity, Gouraud, Phong, and Fast-Phong shading.
Flat shading calculates a single intensity per polygon, useful for curved surfaces. Assumptions for accuracy include object surfaces, light source position, and viewer distance.
Gouraud shading uses intensity interpolation across surfaces, requiring average normals at vertices, leading to smoother transitions without discontinuities.
Intensity at polygon edges is interpolated for scanlines. Gouraud shading can simplify process but may create artifacts like Mach bands, suggesting more polygons or Phong shading.
Phong shading improves realism by interpolating normals. It calculates intensities at pixel points using normal vectors, albeit requiring more computational resources.
Fast Phong shading approximates lighting calculations for efficiency, including specular reflections. It is less time-consuming than traditional Phong shading, though slower than Gouraud.
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Shading methods
- 2. “ Shading isreferred as the implementation of illumination model at the pixel points or polygon surfaces of the graphics objects.”
- 3. A model forinteraction of light with a surface is called an illumination model. Here we concentrate on the location and qualities of the light that falls on the objects and the way in which object intersects with it. There are two types of light sources that illuminate an object:- (1) light - emitting sources (2) light - reflecting sources
- 4. An object isilluminated by light which does not come from any particular source but which comes from all directions that is ambient light. When such illumination is uniform from all directions, the illumination is called diffuse illumination. Diffuse illumination is a background light which is reflected from walls, floor and ceiling. The reflection that is constant over each surface of the object and they are independent of the viewing direction, such a reflection is called diffuse reflection.
- 5. This method weconsider the application of an illumination model to the rendering of standard graphics objects. Each polygon can be rendered with a single intensity or the intensity can be obtained at each point of surface. There are four types of methods:- (1) Constant-intensity Shading (2) Gouraud Shading (1) Phong Shading (1) Fast-Phong Shading
- 6. A fast andsimple method for rendering an object with polygon surfaces is constant intensity shading, also called flat shading. In this method, a single intensity is calculated for each polygon. All points over the surface of the polygon are then displayed with the same intensity value. Constant shading can be useful for quickly displaying the general appearance of a curved surface, as in fig(1)
- 7. Fig(1). A polygonmesh approximation of an object (a) is rendered with flat shading (b) and With Gouraud shading (c). (a) (b) (c)
- 8. In general, flatshading of polygon facets provides an accurate rendering for an object if all of the following assumptions are valid: - 1. The object have many surfaces and is not an approximation of an object with a curved surface 2. All light sources illuminating the objects are sufficiently far from the surface so that is N. and L the attenuation function and these are constant over the surface. (where N is the unit normal to a surface and L is the unit direction vector to the point light source from a position on the surface).
- 9. 3. The viewingposition is sufficiently far from the surface that is V and R is constant over the surface. (where V is the unit vector pointing to the viewer from the surface position and R represent unit vector in the direction of ideal specular reflection). N N1 N N3 V
- 10. This intensity-interpolation scheme,developed by Gouraud and generally referred to as Gouraud shading, renders a polygon surface by linearly interpolating intensity values across the surface. Intensity values for each polygon are matched with the values of adjacent polygons along the common edges, thus eliminating the intensity discontinuities that can occur in flat shading.
- 11. Each polygon surfaceis rendered with Gouraud shading by performing the following calculations: 1. Determine the average unit normal vector at each polygon vertex. 2. Apply an illumination model to each vertex to calculate the vertex intensity. 3. Linearly interpolate the vertex intensities over the surface of the polygon.
- 12. At each polygonvertex, we obtain a normal vector by averaging the surface normal's of all polygons starting that vertex. The normal vector at vertex V is calculated as the average of the surface normal's for each polygon sharing that vertex. 4 N1 N3 V N1 N3 N2
- 13. Thus, for anyvertex position V, we obtain the unit vertex normal with the calculation Once we have the vertex normal's, we can determine the intensity at the vertices from a lighting model.
- 14. Following Figure demonstratesthe next step: interpolating intensities along the polygon edges. For each scan line, the intensity at the intersection of the scan line with a polygon edge is linearly interpolated from the intensities at the edge endpoints. For the example in Fig.(3), the polygon edge with endpoint vertices at positions 1 and 2 is intersected by the scan line at point 4. A fast method for obtaining the intensity at point 4 is to interpolate between intensities I1, and I2 using only the vertical
- 15. displacement of t3he scan line: Y X Scan Line5 2 4 1 Fig(3). For Gouraud shading, the intensity at point 4 is linearly interpolated from the intensities at vertices 1 and2. The intensity at point 5 is linearly interpolated from intensities at vertices 2 and 3. An interior point p is then assigned an intensity value that is linearly interpolated from intensities at positions 4 and 5. 3 P
- 16. Similarly, intensity atthe right intersection of this scan line (point 5) is interpolated from intensity values at vertices 2 and 3. Once these bounding intensities are established for a scan line, an interior point (such as point P in Previous Fig(3)) is interpolated from the bounding intensities at points 4 and 5 as
- 17. Similar calculations areused to obtain intensities at successive horizontal pixel positions along each scan line. When surfaces are to be rendered in color, the intensity of each color component is calculated at the vertices. Gouraud shading can be combined with a hidden-surface algorithm to fill in the visible polygons along each scan line. An example of an object shaded with the Gouraud method appears in following Fig. A polygon mesh approximation of an object (a) is rendered with flat shading (b) and With Gouraud shading (c).
- 18. Gouraud shading removesthe intensity discontinuities associated with the constant-shading model, but it has some other deficiencies. on the surface are sometimes displayed with anomalous shapes, and the linear intensity interpolation can cause bright or dark intensity streaks, called Mach bands, to appear on the surface. These effects can be reduced by dividing the surface into a greater number of polygon faces or by using other methods, such as Phong-shading, that require more calculations.
- 19. A more accuratemethod for rendering a polygon surface is to interpolate normal vectors, and then apply the illumination model to each surface point. This method, developed by Phong Bui Tuong, is called Phong shading, or normal vector interpolation shading. It displays more realistic highlights on a surface and greatly reduces the Mach-band effect. A polygon surface is rendered using Phong shading by carrying out the following steps: 1. Determine the average unit normal vector at each polygon vertex. 2. Linearly & interpolate the vertex normals over the surface of the polygon. 3. Apply an illumination model along each scan line to calculate projected pixel intensities for the surface points.
- 20. Interpolation of surfacenormals along a polygon edge between two vertices is illustrated in Fig.(5). The normal vector N for the scan-line intersection point along the edge between vertices 1 and 2 can be obtained by vertically interpolating between edge endpoint normals. Scan Line N N 3 N 2 Fig.(5) Interpolation of surface normals Along a polygon edge.
- 21. Incremental methods areused to evaluate normals between scan lines and along each individual scan line. At each pixel position along a scan line, the illumination model is applied to determine the surface intensity at that point. Intensity calculations using an approximated normal vector at each point along the scan line produce more accurate results than the direct interpolation of intensities, as in Gouraud shading. The trade-off, however, is that Phong shading requires considerably more calculations.
- 22. Surface rendering withPhong shading can be speeded up by using approximations in the illumination-model calculations of normal vectors. Fast Phong shading approximates the intensity calculations using a Taylor- series expansion and triangular surface patches. Since Phong shading interpolates normal vectors from vertex normals, we can express the surface normal N at any point (x, y) over a triangle as N=Ax+By+C where vectors A, B, and C are determined from the the three vertexequations are: Nk=Axk+Byk+C, k=1,2,3 with (xk,yk) denoting a vector
- 23. Omitting the reflectivityand attenuation parameters, we can write the calculation for light- source diffuse reflection from a surface point (x, y) as
- 24. ax+by+c (dx2+exy+fy2+gx+hy+i)1/2 eq(1 ) T5x2+T4xy+T3y2+T2x+T1y+T0 eq(2) where eachTk, is a function of parameters a, b, c, and so forth. Idiff(x,y) = Idiff(x,y) = where parameters such as a, b, c, and d are used to represent the various dot products. For example a= L.A |L| Finally, we can express the denominator in Eq. (1) as a Taylor-series expansion and retain terms up to second degree in x and y. This yields We can rewrite this expression in the form
- 25. Using forward differences,we can evaluate Eq. (2) with only two additions for each pixel position (x, y) once the initial forward-difference parameters have been evaluated. Although fast Phong shading reduces the Phong- shading calculations, it still takes approximately twice as long to render a surface with fast Phong shading as it does with Gouraud shading. Normal Phong shading using forward differences takes about six to seven times longer than Gouraud shading.
- 26. Fast Phong shadingfor diffuse reflection can be extended to include specular reflections. Calculations similar to those for diffuse reflections are used to evaluate specular terms such as (N.H)ns in the basic illumination model. In addition, we can generalize the algorithm to include polygons other than triangles and finite viewing positions.