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Introduction to Computer Graphics

Introduction to Computer Graphics. Chapter 6 – 2D Viewing Pt 3. Nicholl-Lee-Nicholl Line Clipping (NLN). Creating more regions around the clip window to avoid multiple clipping of an individual line segment.

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Introduction to Computer Graphics

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  1. Introduction to Computer Graphics Chapter 6 – 2D Viewing Pt 3

  2. Nicholl-Lee-Nicholl Line Clipping (NLN) • Creating more regions around the clip window to avoid multiple clipping of an individual line segment. • Different to Cohen where Cohen require multiple calculation along the path of a single line before an intersection on the clipping rectangle is locate or completely rejected. • NLN eliminate extra calculations through new region created.

  3. Nicholl-Lee-Nicholl Line Clipping (NLN) • Compared to Cohen and Liang; • NLN perform fever comparisons and division. • The trade-off is that NLN can only be applied two two-dimensional clipping only.

  4. Nicholl-Lee-Nicholl Line Clipping (NLN) • How its work? • First , need to determine the endpoints P1 and P2 from the possible nine regions. • Out of nine, NLN only interested on three regions. • If P1 lies in any one of other six regions, symmetry transformation will be applied first. • Then, is to determine where P2 is. • If P1 is inside and P2 is outside we will follow the first case where intersection with appropriate window boundary is carried out. Four regions of L,T,R,B which contains P2 are introduced. • If P1 and P2 are inside the clipping rectangle, we save the entire line.

  5. NLN L L L P2 (6,7) (2,6) LT (6,6) LR P1 (1,4) LB (2,2) (6,2)

  6. NLN • For example when P2 is in region LT if Slope P1PTR < Slope P1P2 < Slope P1PTL • Or (YT - Y1)/(XR – X1)) < (Y2 - Y1)/(X2 – X1) < (YT – Y1)/(XL – X1) • Ex: • (6-4)/(6-1) < (7-4)/(6-1) < (6-4)/(2-1) • 2/5 < 3/5 < 2 And we clip the entire line if  (YT – Y1)(X2 – X1)< (XL – X1)(Y2 – Y1)

  7. NLN • From the parametric equations: x = x1 + (x2 – x1)u y = y1 + (y2 – y1)u • An intersection position on the left boundary is x = xLwith u = (xL – x1)/(x2 – x1)will give coordinate y = y1 +((y2 – y1)/(x2 – x1)) * (xL – x1) • An intersection position on the top boundary has y = yT with u = (yT – y1)/(y2 – y1) will give coordinate x = x1 +((x2 – x1)/(y2 – y1)) * (yT – y1)

  8. Line Clipping Using Nonrectangular Clip Windows • Some applications clip lines against arbitrarily shaped polygons. • Liang and Cyrus-Beck algorithm can be extended to convex polygon windows. • For concave polygon-clipping regions, we need to split the concave polygon into set of convex polygons. • Circles or other curved-boundary clipping regions are also possible but slower because intersection calculations involve nonlinear curve equation. • Line can be identified as completely inside if the distance for both endpoints of a line is less than or equal to the radius squared. • If not, then intersection calculation is performed.

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