Ray-triangle intersection
Ray-triangle intersection Brian Curless April 2004 In this handout, we explore the steps needed to compute the intersection of a ray with a triangle First, we consider the geometry of such an intersection: d A B C P Q where a ray with origin P and direction d intersects a triangle defined by its vertices, A, B, and C at intersection point Q
Chapter 11 Geometrics
P O T Point on tangent outside the effect of any curve P O C Point on a circular curve P O S T Point on a semi-tangent (within the limits of a curve) P I Point of intersection of a back tangent and forward tangent P C Point of curvature - Point of change from back tangent to circular curve
2 Distance dun point à une droite - Maurimath
d'intersection : E et F On dit que (D) est sécante à C en E et F Définition : Si (D) et C ont un point commun et un seul M, on dit que (D) est tangente à C en M 5 Tangentes et bissectrices Propriété de la bissectrice d'un angle: Si un point est sur la bissectrice d'un angle alors il est équidistant des droites portant les côtés de
Segment-Segment Intersection
Segment-Segment Intersection 1 For many application, the floating-point coordinates of the point of intersection are needed 2 We will need this to compute the intersections between two polygons 3 Let the two segments have endpoints a and b and c and d, and let L ab and L cd be the lines containing the two segments 4
101 Lines and Segments That Intersect Circles
c DE ⃗ d ⃖AE ⃗ SOLUTION a AC — is a radius because C is the center and A is a point on the circle b AB — is a diameter because it is a chord that contains the center C c DE ⃗ is a tangent ray because it is contained in a line that intersects the circle in exactly one point d
Lecture 1: Introduction and line segment intersection
A point, line, circle, ::: requires O(1), or constant, storage A simple polygon with n vertices requires O(n), or linear, storage Geometric Algorithms Lecture 1: Introduction and line segment intersection
Everything you ever wanted to know about collision detection
– Plug test point into plane equation for all 6 faces – If all test results have the same sign, the point is inside (which sign depends on normal orientation, but really doesn’t matter) • Smart Plane Equations Test – Each pair of opposing faces has same normal, only d changes – Test point against d intervals – down to 3 plane tests
Bisectors of Triangles
The point of concurrency is the circumcenter of the triangle Circumcenter Theorem Given ABC; the perpendicular bisectors of AB —, BC —, and AC — Prove The perpendicular bisectors intersect in a point; that point is equidistant from A, B, and C Show that P, the point of intersection of the perpendicular bisectors of AB — and BC —
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