By Ramakrishnan Mukundan
This ebook brings jointly numerous complex subject matters in special effects which are very important within the components of online game improvement, three-d animation and real-time rendering. The ebook is designed for final-year undergraduate or first-year graduate scholars, who're already acquainted with the elemental techniques in special effects and programming. It goals to supply an excellent beginning of complicated equipment resembling skeletal animation, quaternions, mesh processing and collision detection. those and different tools coated within the e-book are basic to the improvement of algorithms utilized in advertisement purposes in addition to research.
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Extra info for Advanced Methods in Computer Graphics: With examples in OpenGL
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. 48 can be computed by applying the formula in Eq. 8 to each of the triangles QP2 P3 , QP3 P1 , QP1 P2 and P1 P2 P3 . If the conditions œ1 C œ2 C œ3 D 1, 0 Ä 1 , 2 , 3 Ä 1 24 2 Mathematical Preliminaries are met, then Q lies on the plane defined by the points P1 , P2 , P3 , and also lies within the triangle P1 P2 P3 .
43) An interesting variation of the above equation can be derived by expressing the parameter t as a function of an angle ’, given by t D cos2 ’. Then the coefficient (1 t) becomes sin2 ’, and Eq. 43 takes the form Q D sin2 ’ P1 C cos2 ’ P2 . However, this trigonometric interpolation formula gives a non-uniform distribution of points on the line when ’ is varied from 0ı to 90ı in equal steps. A comparison of linear and trigonometric interpolations is given in Fig. 10. In Fig. 1, and in Fig. 10b, the angle ’ is varied uniformly in the range [0–90] in steps of 9ı .
On the other hand, OBBs and spheres are rotation invariant. In this chapter, examples are provided using AABBs and spheres only. Other types of bounding volumes and their computational aspects are discussed in detail in Chap. 9. Since the bounding volume parameters depend on the transformed object coordinates, bounding volume updates can be performed only after applying the transformations. 4 Bounding Volume Hierarchy 41 Fig. 14 Two-dimensional bounding volume hierarchies for the model in Fig. 2, using axisaligned rectangles (top row) and circles (bottom row) a b c Fig.
Advanced Methods in Computer Graphics: With examples in OpenGL by Ramakrishnan Mukundan