Object space algorithm: Back-Face removal. · No faces on the back of the object are displayed. · In general – about half of objects faces are back faces. Computer Graphics Lecture 8 Hidden Surface Removal Taku Komura 1 1 Or if N.V > 0 we are viewing the back face so polygon is obscured. . Tree construction and traversal (object-space ordering algorithm – good for relatively few static. Occluded surfaces: hidden surface removal (visibility). ▫ Back faces: back face culling. ▫ Faces OpenGL): Z-buffer (or depth buffer) algorithm. ▫ Requires lots .

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Right Handed coordinate System. Point 2 – 1. Point 3 – 2. Standard equation of a plane in 3 space: Normal to the plane is the vector A ,B,C.

## Visible Surface Detection

Given three points in space x1 ,y1,z1x2,y2,z2x3,y3,z3 the equation of the plane through these points is given by. Begin with a system of linear equations, for example, a system involving three variables. There are two other matrices obtained by replacing the coefficients in each column by the constants c 1 and c 2 respectively.

Their determinants are det A x and det A y respectively. For a 3 x 3 matrix of coefficients the determinant may be expressed as either:.

### Computer Graphics Visible Surface Detection

If the 3 points are collinear then the normal A ,B,C will be 0,0,0. Calculating Normal using plane equations. Same as with normal vector. Begin at top vertex of polygon.

Recursively calculate x-coordinate values down left edge of baackface. Subsequent x-values for each scanline calculated from starting x-value. Surface color and pixel coverage.

Simplest to use maximum z value. Front, Back and On lists — done by comparing the normal vector of the plane with that of each polygon. If the eye is in front of the root, then. Display the left subtree behind.

### Hidden Surface Removal – ppt download

Display the right subtree front. If eye is algortihm back of the root, then. Display the left subtree back. Ray casting is easy to implement for polygonal models because the only calculation required is the intersection of a line with a plane.

For a 3 x 3 matrix of coefficients the determinant may be expressed as either: Used only for solid objects modeled as a polygon mesh. Problematic for concave polyhedra.

Begin at top vertex of polygon 2. Recursively calculate x-coordinate values down left edge of polygon 3. Partition all the other polygons in the scene to the back left subtree or the front right subtree.

Split any polygons lying on both sides of the root see below.

## Back Face Removal

Build the left and right subtrees recursively. Ray Casting Algorithm Through each pixel, fire a ray to the eye: Intersect the ray with each polygonal plane. Reject intersections that lie outside the polygon.

Accept the closest remaining intersection — that is, the intersection with the smallest value of the parameter along the line. The main advantage of the ray casting algorithm for hidden surfaces is that ray casting can be used even with non-polygonal surfaces.

The main disadvantage of ray casting is that the method is slow. Ray casting is a brute force technique that makes no use of pixel algoritym.