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Additional info for Advanced Methods in Computer Graphics: With examples in OpenGL
It is therefore often desirable that the parameters defining a bounding volume stored at a group node can be computed based on the bounding volume parameters of its child nodes. It should also be noted here that such a computation may not always yield a minimal bounding volume. For example, the bounding sphere computed as the union of two bounding spheres may not necessarily be the minimal bounding sphere for the union of points within those spheres. A two-dimensional equivalent of this case is shown in Fig.
4 Class definition for a light node sources GL LIGHT0, : : : ,GL LIGHT7. In OpenGL, light sources are transformed like any other point. The function draw() defines the initial position of the light source at (0,0,0), and transforms it exactly like its counterpart in ObjectNode. The class does not store or set any other light or material properties. They can be set by the application by directly calling the appropriate OpenGL functions. The same applies to setting OpenGL states such as enabling lighting, selecting two sided lighting, enabling colour material, and so on.
Thus barycentric coordinates find applications in point inclusion tests. In a general three-dimensional case, however, the area of a triangle computed using Eq. 3 would always be positive, and correspondingly the area ratios in Eq. 48 would also be positive. As previously discussed in Sect. 2, the computation of signed areas of triangles requires a view vector w. Since we need this vector to be fixed with respect to every triangle in Eq. 48, we can conveniently choose w D (P2 P1 ) (P3 P1 ). Now the barycentric coordinates 1 , 2 and 3 in Eq.