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Unformatted text preview: I N T R O D U C T I O N T O C O M P U T E R G R A P H I C S Andries van Dam October 1st, 2009 2D Clipping 1/16 Clipping I N T R O D U C T I O N T O C O M P U T E R G R A P H I C S Andries van Dam October 1st, 2009 2D Clipping 2/16 Clipping Chapter 13, Section 10 I N T R O D U C T I O N T O C O M P U T E R G R A P H I C S Andries van Dam October 1st, 2009 2D Clipping 3/16 Line Clipping • Clipping endpoints x min < x < x max and y min < y < y max point inside • Endpoint analysis for lines: – if both endpoints in , do “trivial acceptance” – if one endpoint inside, one outside, must clip – if both endpoints out, don’t know • Brute force clip: solve simultaneous equations using y = mx + b for line and four clip edges – slopeintercept formula handles infinite lines only – doesn’t handle vertical lines (X min , Y min ) (X max , Y max ) I N T R O D U C T I O N T O C O M P U T E R G R A P H I C S Andries van Dam October 1st, 2009 2D Clipping 4/16 Parametric Line Formulation For Clipping • Parametric form for line segment X = x + t(x 1 – x ) 0 < t < 1 Y = y + t(y 1 – y ) P(t) = P + t(P 1 – P ) • “true,” i.e., interior intersection, if s edge and t line in [0,1] I N T R O D U C T I O N T O C O M P U T E R G R A P H I C S Andries van Dam October 1st, 2009 2D Clipping 5/16 • Divide plane into 9 regions • Compute the sign bit of 4 comparisons between a vertex and an edge – y max – y; y – y min ; x max – x; x  x min – point lies inside only if all for sign bits are 0, otherwise exceeds edge • 4 bit outcode records results of four bounds tests: First bit : outside halfplane of top edge, above top edge Second bit : outside halfplane of bottom edge, below bottom edge Third bit : outside halfplane of right edge, to right of right edge Fourth bit : outside halfplane of left edge, to left of left edge • Lines with OC = 0 and OC 1 = 0 can be trivially accepted • Lines lying entirely in a half plane outside an edge can be trivially rejected : OC AND OC 1 ≠ 0 (i.e., they share an “outside” bit) Outcodes for CohenSutherland Line Clipping in 2D Clip Rectangle I N T R O D U C T I O N T O C O M P U T E R G R A P H I C...
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This note was uploaded on 10/23/2009 for the course PPT cs taught by Professor Nil during the Spring '09 term at Indian School of Business.
 Spring '09
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