Team LRN in .NET Integrate Code 128 in .NET Team LRN

Team LRN use visual studio .net code 128 code set c encoding tobuild code 128b with .net .NET Framework Intersection Testing u p q Figure X.2 .net framework Code-128 .

The ray speci ed by its start position p and direction u intersects the plane at the point q.. the compli cated object, you can rst test whether the ray intersects the bounding sphere. If not, then it also does not intersect the geometric object. However, if the ray does intersect the bounding sphere, you must further test for intersection with the geometric object.

The advantage of the bounding sphere is that it allows you to detect many cases of nonintersection quickly.. Exercise X code128b for .NET .1 Write an ef cient pseudocode algorithm for bounding sphere testing.

[Hint: Use the rst part of the ray sphere intersection algorithm, namely, the part through line 6 ending with the test for b2 > r 2 . Finish up by testing the condition > 0 or 2 a 2 . ] An ellipsoid is speci ed by its center, three orthogonal axes, and three Exercise X.

2 radii. The three orthognal axes and radii can be speci ed by three orthogonal vectors v1 , v2 , and v3 , with each norm . vi equal to VS .NET Code 128 the inverse of the radius in the direction of vi : the ellipsoid is the set of points x such that i ((x c) vi )2 = 1. Formulate an ef cient ray versus ellipsoid intersection algorithm.

. X.1.2 Ray versus Plane Intersections A plane is visual .net ANSI/AIM Code 128 speci ed by a normal vector n perpendicular to the plane and a scalar d. The plane is the set of points x satisfying x n = d.

If p and u specify a ray as usual, then, to intersect the ray with the plane, we rst calculate the point q (if it exists) that is the intersection of the ray-line with the plane. This q will equal p + u for a scalar. To lie in the plane, it must satisfy d = q n = p n + u n.

Solving for yields d p n . u n The quantities in this formula for all have geometric meaning. If n is a unit vector, then the value d p n is the negative of the distance of p above the plane, where above means in the direction of n.

For nonunit n, (d p n)/. n. is the ne Code-128 for .NET gative of the distance of p above the plane. In particular, p is above (respectively, below) the plane if and only if d p n is negative (respectively, positive).

The dot product u n is negative if the ray s direction is downward relative to the plane (with n de ning the notions of down and up ). If u n = 0, then the ray is parallel to the plane, and the usual convention is that in this case the ray does not intersect the plane at all. Even if the ray lies in the plane, it is usually desirable for applications to treat this as not intersecting the plane.

The value of is the signed distance of q from p. If < 0, then the ray does not intersect the plane. =.

Team LRN X.1 Fast I barcode code 128 for .NET ntersections with Rays These considerations give the following ray-versus-plane intersection algorithm:.

Ray-Plane Intersection: Input: p and unit vector u de ning a ray. n and d de ning a plane. Algorithm: Set c = u n; If ( c == 0 ) { Return No intersection (parallel) ; } Set = (d p n)/c; If ( < 0 ) { Return No intersection ; } Set q = p + u; Return q;.

Sometimes visual .net USS Code 128 we want to intersect the ray-line against the plane instead, such as in the ray versus convex polytope intersection algorithm in Section X.1.

4. This is even simpler than the previous algorithm, for we just omit the test for 0:. Line-Plane Intersection: Input: p and unit vector u de ning a line. n and d de ning a plane. Algorithm: Set c = u n; If ( c == 0 ) { Return No intersection (parallel) ; } Set = (d p n)/c; Set q = p + u; Return q;.

Exercise X Code 128C for .NET .3 What would happen if we drop the requirement that the vector u be a unit vector Show that the preceding algorithms would still compute the intersection point q correctly, but not the distance .

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