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Computer Graphics

Chapter 9Rendering

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Rendering

Three dimensional object rendering is the set of collective processes which make the object model appear more realistic on the display screen. These processes include

The elimination of surfaces (polygonal segments) on the object that are not visible with respect to the user’s view direction.

Incorporating shading and shadowing effects.

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Computing Surface Normal

P3

P1 P2

V1

V2

N V1 = P2P1 = (x2x1, y2y1, z2z1).

V2 = P3P1 = (x3x1, y3y1, z3z1).

N = V1 V2.

131313

121212

zzyyxx

zzyyxx

kji

Surface Normal:

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Components of Surface Normal

Nx = (y2y1) (z3z1) (y3y1) (z2z1)

Ny = (z2z1) (x3x1) (z3z1) (x2x1)

Nz = (x2x1) (y3y1) (x3x1) (y2y1)

Nx = y1(z2-z3)+ y2(z3-z1)+ y3(z1-z2)

Ny = z1(x2-x3)+ z2(x3-x1)+ z3(x1-x2)

Nz = x1(y2-y3)+ x2(y3-y1)+ x3(y1-y2)

OR

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Back-Face Culling

ZViewer

Back faces

Nz < 0 The polygon is hidden

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Back-Face Culling - Limitations

Requires specific ordering of the vertices in the polygon table to determine the outward normal direction.

The algorithm will work only with convex objects.

A polygon is either completely displayed, or totally eliminated from the display.

+Viewer

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Back-Face Culling (General Case)

Viewer P1

P2V

N

V.N > 0 The polygon is hidden

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Back-Face Culling (Example)

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Back-Face Culling (OpenGL)

Defining a front face as the face with CCW ordering of vertices(Default):

glFrontFace(GL_CCW);

Enabling polygon culling:

glEnable(GL_CULL_FACE);

Discard back facing polygons:

glCullFace(GL_BACK);

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Painter’s Algorithm

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Painters Algorithm

Basic Steps:

Sort polygons in the ascending order of z-coordinates

Fill polygons in the sorted order.

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Painters Algorithm - Limitations

Requires sorting of polygons.

All polygons must be necessarily filled.

May lead to erroneous images if a failure condition (see below) occurs.

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Polygons with depth and region overlap.

Z

(1)

(2)

Polygons having both depth-overlap and region overlap may requirere-sequencing of the polygonsin the sorted list.

Painters AlgorithmFailure Conditions (1)

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Polygons with cyclic overlap.

Painters AlgorithmFailure Conditions (2)

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Painter’s AlgorithmIllustration of failure conditions

Wrong Correct

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Z

Depth-Buffer Algorithm

Frame Buffer Depth Buffer

Color ValueMinimum Depth Value

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Depth-Buffer Algorithm

For each pixel (i, j), a line passing through the pixel and the viewer is considered, and the depths of the polygons on this line are computed.

The value d(i, j) in the depth buffer contains the pseudo-depth of the closest polygon encountered at pixel (i, j).

The value p(i, j) in the frame buffer (the color of the pixel) is the color of the closest polygon.

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Depth-Buffer Algorithm

Limitations: The algorithm requires a large amount of

additional memory to store the pseudo depth at each pixel value.

Since the analysis is based on a point by point test, the algorithm is time consuming.

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Shading Models

A shading model dictates how light is scattered or reflected from a surface.

A surface is shaded by adjusting the color intensity value of each polygon according to the shading algorithm.

Main components: Light source vector, surface normal vector,

viewer direction. Material characteristics of the surface The illumination model.

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Shading ModelsVectors

ms

v

Polygon

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Shading ModelsSurface Properties (1)

abs (Coeff. of absorption): Specifies how much of the incident light is absorbed. If all of the incident light is absorbed, the object appears black.

spec (Coeff. of specular reflection) Specifies how much of the incident light is specularly reflected in one direction. For a highly reflective surface such as a mirror, the value is close to 1.0

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Shading ModelsSurface Properties (2)

diff (Coeff. of diffuse reflection): Diffuse scattering occurs when the incident light is re-radiated uniformly in all directions. For a rough non-reflective surface, the value is close to 1.0.

amb (Coeff. of ambient reflection): Specifies how much of the ambient light is reflected by the surface. Often this is same as the diffuse reflection coefficient diff.

abs + spec +diff = 1.0

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I

If I is the incident light intensity,then I abs is absorbed by the surface.

I spec is specularly reflected.

I diff is diffusely reflected.

Surface Properties

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Surface Element

AmbientLight

AmbientLight

Point Source

Illumination Models

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Illumination ModelsAmbient Light

Produces uniform illumination (also known as background light).

Has no spatial or directional characteristics. Assumed to be incident from all directions

with constant intensity Ia.

Ambient light reflection from a surface is constant along all visible directions, and does not depend on the surface orientation.

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Illumination ModelsPoint Light Source

Defined in terms of both the position of the source, and the intensity of the source Is.

The reflection from a point light source depends on the surface orientation, and varies with respect to the view direction.

Light source reflection consists of both specular reflection and diffuse reflection.

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Light Perceived by the ViewerDiffuse Reflection

Point Source

Id = Is diff cos

Since diffuse scattering is uniform in all directions, the orientation of the polygon relative to the viewer is not significant.

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Light Perceived by the ViewerSpecular Reflection

The vector h = s + v is known as the half-way vector.

f is an experimentally determined constant

Isp = (Is spec cos f )

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Light Perceived by the ViewerSpecular Reflection

f is specular reflection parameter determine is specular reflection parameter determine type of surface. (in OpenGL the value range 0 type of surface. (in OpenGL the value range 0

to 128). A very shiny surface is modeled with a to 128). A very shiny surface is modeled with a large value, and smaller value (down to 0) are large value, and smaller value (down to 0) are

used for dull object.used for dull object.

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Light Perceived by the ViewerAmbient Reflection

Ambient reflection is independent of surface orientation.

Ambient reflection is independent of viewers position.

The ambient light Ia is uniformly reflected with intensity Ia amb. This is denoted as the ambient reflection Iamb.

Iamb = Ia amb

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Computation of Total Reflected Light

Total light intensity perceived by the user

= Iamb+ Isp + Id

= (Ia amb) + (Is spec cos f ) + Is diff cos

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Shading (OpenGL)

Setting material properties in OpenGL:

glMaterialfv(GL_FRONT, refl, iarray);

where, refl = GL_AMBIENT :Sets ambient reflection coefficients.GL_DIFFUSE : Sets diffuse reflection coefficients.GL_SPECULAR : Sets specular reflection coefficients.

iarray : Array of coefficients in RGBA format.

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Flat and Smooth Shading

The entire polygon is drawn with the same shade or color.

The shades at the vertices are interpolated to determine the shade at an interior point

Flat Shading Gouraud Shading

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Gouraud Shading

The color at P1 is obtained by linearly interpolating the colors C1 and C2.

Similarly, the color at P2 is found by linearly interpolating the colors C3 and C4.

Having found P1 and P2, the algorithm then fills along the scan line by linearly interpolating between P1 and P2 to determine the color at an intermediate pixel Q.

y C1

C2

C3

C4

P1 P2Q

yk

x

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Flat and Smooth Shading (OpenGL)

Setting flat shading:

glShadeModel(GL_FLAT);

Setting Gouraud shading:

glShadeModel(GL_SMOOTH);

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Flat and Smooth Shading

Gouraud shading provides a much smoother appearance of surfaces.

Flat Shading Gouraud Shading

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Texture Mapping (Examples)

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Texture Mapping

The basic techniques begin with some texture functions, texture(s,t),in texture space which is traditionally marked off by parameters named s and t.

The function texture(s,t) produces a color or intensity value for each value of s and t between 0 and 1.

Texture mapping is the process of mapping a region in the 2D texture space to a region in the 3D space defined by the boundary points.

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Texture Mapping

Texture Space

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Texture Mapping (OpenGL)

Associating a point (s,t) in texture space with avertex V(x,y,z) of a polygon:

glTexCoord2f(s, t);glVertex3f(x, y, z);

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Texture types

Bitmap Textures: Often formed from bitmap representations of images.

Defined by a mathematical function or procedure.