Solid Area Scan Conversion or Visible Surface Detection

P (viewing point)

visible-surface detection Given a set of 3 D object and viewing point This process find which lines or parts of the object are visible from the viewing point , So that it can draw only those part Find which surfaces are visible-surface detection Remove those surfaces that should not be visible hidden-surface removal.

Visible Surface Detection algorithm • Visible surface detection algorithms are broadly classified as: – Object Space Methods: Compares objects and parts of objects to each other within the scene definition to determine which surfaces are visible – Image Space Methods: Visibility is decided pointby-point at each pixel position on the projection plane • Image space methods are by far the more common

Visible Surface Detection algorithm contd… Two main types of algorithms: – Object space: Determine which part of the object are visible – Image space: Determine per pixel which point of an object is visible Object space Image space

Visible surface detection algorithms are based on following 2 concepts: – Sorting : It facilitate the depth comparison by ordering the object surface or lines in the scene according to their distance from the view plane – Coherence : This method are used to take advantage of regularities in a scene ( It contain intervals of constant pixel intensity & scan pattern change (a little), from one line to other)

Visible Surface Detection Algorithms • • • Depth Comparison Z-buffer or Depth Buffer Depth Sorting or Painter’s Area Subdivision or Warnock’s Back Face detection A – Buffer Scan line BSP tree OCTree

Z-Buffer(Extension of frame buffer) (Image space) • Frame buffer stores the intensity value of each pixel in image space. • Z-buffer(depth buffer) stores the z-coordinate value of each pixel in image space. When an object in 3 D is projected on a view plane as projection pt(x, y) it’s z-value is compared with the previously stored z-value. If it is smaller then new pixel is written to the frame buffer and z-buffer is updated with new z-value

S 3 S 2 y axis S 1 Z 3 Z 2 Z 1 x axis z axis Order of scanning is S 2 s 3 s 1

Two buffers are needed: depth and color. – Initialize the buffers: depth(x, y) = Zbackground color(x, y) = Ibackground –For (each position on each polygon surface) calculate z for each (x, y)position if (z(x, y) < depth(x, y)) { depth(x, y) = Z color(x, y) = Isurf }

Painter’s algorithm (image space & object space) This algorithm process the polygon as if they were being painted into the screen in order of their distance from the viewer. It has following basic steps v Surface are sorted in order of decreasing depth v Surface are scan converted in order, starting with surface of greatest depth.

By Painter’s Algorithm

STEP 1 Store the polygon in array by uniquely numbering them 1 2 3 4 5 6 1 6 2 4 5 3 STEP 2 For each polygon maintain a linked list named as front list which will contain the polygon no. in front of it in a sequence STEP 3 For each polygon maintain a counter named as behind counter which will contain the no. of polygon behind to it

6 n o i ti ia In t a liz Polygon Array 1 2 3 4 5 6 2 1 Front List 5 4 5 3 Behind Counter 2 4 3 1 0 1 5 3 2 1 2 0

STEP 4 (loop) Repeat step 5 & step 6 till all polygon behind counter is -1 STEP 5 Draw all polygon’s whose behind counter is 0 STEP 6 After drawing a) Step through the polygon in the front list, decrease their behind counter by 1. b) For drawn polygon make it’s behind counter as -1

6 ITERATION -- 1 2 Polygon Array 1 2 3 4 5 6 New Front List Behind Counter 1 2 5 4 3 1 0 -1 1 5 3 2 1 1 2 0 -1

6 ITERATION -- 2 2 Polygon Array 1 2 3 4 5 6 4 New Front List Behind Counter 1 1 5 4 3 1 -1 1 5 3 1 -1 0 0 2 -1 -1

6 ITERATION -- 3 2 Polygon Array 1 2 3 4 5 6 4 3 New Front List Behind Counter 1 0 5 4 3 1 -1 1 5 3 0 -1 -1 -1 2 -1 1 -1 -1

6 ITERATION -- 4 2 1 Polygon Array 1 2 3 4 5 6 4 3 New Front List Behind Counter 0 -1 5 4 3 1 -1 1 5 3 -1 -1 0 -1 -1

6 ITERATION -- 5 2 1 Polygon Array 1 2 3 4 5 6 4 5 3 New Front List Behind Counter -1 -1 5 4 3 1 -1 1 5 3 -1 -1 0 -1 -1

Depth-Sorting Algorithm 1 Summary • Image and Object space • Sort surfaces for depth • Draw them back to front H&B 16 -6: 511 -514

Disadvantage For following type of polygons this will not work Solution • Cyclically overlapping polygons require cutting • Piercing polygons require clipping

Back-face Detection or Elimination • A point (x, y, z) is “inside” a surface with plane parameters A, B, C, and D if • A point (x, y, z) is “outside” a surface with plane parameters A, B, C, and D if • We cannot see the back-face of solid objects: Hence, these can be ignored

Back-face elimination The polygon is a front face if V N Where, • V is a vector in the viewing direction from the eye(camera) • N is the normal vector to a polygon surface

Back-face elimination The polygon is a back face if N V Where, • V is a vector in the viewing direction from the eye(camera) • N is the normal vector to a polygon surface

Back-face elimination • Object-space method • Works fine for convex polyhedra: ± 50% removed • Concave or overlapping polyhedra: require additional processing • Interior of objects can not be viewed Partially visible front faces