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Lecture 12 - Spline surfaces (slides)

# G we select a grid of points eg 00 01 02

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Unformatted text preview: ues of 0 or 1 for µ and/or ⌫ we can easily verify Substituting values of 0 or 1 for µ that the equation ﬁts the edge curves. and/or ν we can easily verify that the equation ﬁts the edge curves. ! ! Graphics Lecture 12: Slide 19! 19 / 35 Rendering a patch: Polygonisation Rendering a patch: Polygonisation " To render (draw) a spline patch we can simply transform it i render (draw) ! Tonto polygons. a spline patch we can simply transform it into polygons. We select a grid of points, e.g.: ! We select a grid of points, eg: µ = {0.0, 0.1, 0.2, . . . 1.0} ⌫ = {0.0, 0.1, 0.2, . . . 1.0} and triangulate to that grid. and triangulate to that grid. ! Graphics Lecture 12: Slide 20! 20 / 35 Rendering a patch: Polygonisation " Rendering a patch: Polygonisation •  For speedwe can use large polygonspolygons withPhong For speed we can use large with Gouraud or Gouraud or shading. Phong shading. ! •  For accuracy we use small polygons, chosen to match For accuracy we use small polygons, chosen to match the pixel size. the pixel size. ! 21 / 35 Graphics Lecture 12: Slide 21! aces can also be drawn by a technique called lofting (now Rendering a patch: Lofting " ly obsolete). •  Surfaces can also be drawn by a technique called lofting (now really obsolete). ! means •drawing contours of constant µ µ and/or ofof constan and/or   This means drawing contours of constant constant ν •  Algorithms for eliminating the hidden parts have been rithms for eliminating the hidden parts have been devised. devised. ! Graphics Lecture 12: Slide 22! Rendering a patch: Ray tracing Rendering a patch: Ray tracing " The patch equation is fourth order order ! •  The patch equation is fourth P(µ, ⌫ ) = P(µ, 0)(1 ⌫ ) + P(µ, 1)⌫ + P(0, ⌫ )(1 µ) + P(1, ⌫ )µ P(0, 1)(1 µ)⌫ P(0, 0)(1 µ)(1 P(1, 0)µ(1 ⌫) ⌫) P(1, 1)µ⌫ •  Hence no closed form solution exists for a ray patch intersection ! •  Can numeric algorithms but computation can be can Can use use numeric algorithms but comput...
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