raud-Sháding Intérpòlatión Gouraud shading is performed by linearly interpolating the colors of the vertices of a polygon to the points in the interior of the polygon. Consider the triangle in the figure below with vertices at (0, 0), (1, 0) and (0, 1). Let CO, C1, C2 denote the corresponding RGB color vectors assigned to these three vertices. (1) Derive a linear interpolation function C(x, y) which maps a point Q = (x, y) in the triangle to an RGB color vector by blending these three colors together. The final color should be a function of x, y and C0, Cı, C2. Show your work. (0,1)C2 Q-(x.y) (0,0). .Cl (1,0) CO 2) CO, C(1, 0) = Ci , C(0, 1) = C2 . Verify the correctness of your function by demonstrating that C(0, 0) =

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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Chapter1: Introduction
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Gouraud-Shading Interpolation
Gouraud shading is performed by linearly interpolating the colors of the vertices of
a polygon to the points in the interior of the polygon. Consider the triangle in the
figure below with vertices at (0, 0), (1, 0) and (0, 1). Let C0, C1, C2 denote the
corresponding RGB color vectors assigned to these three vertices.
(1)
Derive a linear interpolation function C(x, y) which maps a point Q = (x,
y) in the triangle to an RGB color vector by blending these three colors together.
The final color should be a function of x, y and CO, Ci, C2. Show your work.
(0,1)C2
Q-(x,y)
(0,0).
CO
Cl
(1,0)
(2)
Verify the correctness of your function by demonstrating that C(0, 0) =
CO, C(1, 0) = C1 , C(0, 1) = C2 .
Transcribed Image Text:Gouraud-Shading Interpolation Gouraud shading is performed by linearly interpolating the colors of the vertices of a polygon to the points in the interior of the polygon. Consider the triangle in the figure below with vertices at (0, 0), (1, 0) and (0, 1). Let C0, C1, C2 denote the corresponding RGB color vectors assigned to these three vertices. (1) Derive a linear interpolation function C(x, y) which maps a point Q = (x, y) in the triangle to an RGB color vector by blending these three colors together. The final color should be a function of x, y and CO, Ci, C2. Show your work. (0,1)C2 Q-(x,y) (0,0). CO Cl (1,0) (2) Verify the correctness of your function by demonstrating that C(0, 0) = CO, C(1, 0) = C1 , C(0, 1) = C2 .
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