Object models for computer aided design

Page 19

2j􁪽􋴚􁪽􋴚􁪽􋴚􁪽􋵣c􁪽􋵡al 􁪽􋴚􁪽􋵦forrra􁪽􋵩io􁪽􋵴 tne accuracy of t􁪽􋵥e ore reserve ca::􁪽􋴱12tio􁪽􋵣 ca􁪽􋵢 be irr;rove􁪽􋴵 5iqn􁪽􋵦f􁪽􋵣ca􁪽􋵴tly. Ho􁪽􋵥ever, even 􁪽􋵩it􁪽􋵡 a 􁪽􋵯odelinq systerr this 􁪽􋵲rocess 􁪽􋴵5 ne􁪽􋵴ther :r􁪽􋵶vial nor fast. reserves are calc􁪽􋵬lated for an eic!vation or ring by cOffiputing an average of a lar􁪽􋵥e nu􁪽􋵢ber of $a􁪽􋵆Fle points 􁪽􋵨hicM are within the volume. The grade for each of the sarr;le points is in turn an average of 􁪽􋵬ll of the assays 􁪽􋵨hich are near the point and lie in T􁪽􋵥ese assays are 􁪽􋵥eigtted by 1/02, w􁪽􋵥ere d is the distance frorr the sample point to the assay. To illustrate the derrands such a calculation puts on the modeling system, we 􁪽􋵩ill consider the problerr of deterrrining whether the sa􁪽􋵰ple point is inside an arbitrary 􁪽􋵯oljhEd:on (both excavations and rings can be represented t-::' such polyhedra). The II inside/outside" algorithm for a intersection of an 2rb􁪽􋵴trary ray drawn fro􁪽􋵴 the point 􁪽􋵩ith each face cf the ;o2.y:-.eorcn. If the r.u􁪽􋵢ber of i􁪽􋵴tersections :5 ode, pcint rr.ust be inside. The intersecticn of the ray with the face again invol􁪽􋵥es a 2D inside/outside test which reouires co􁪽􋵮nting the intersections of a ray constructed frorr the intersection of the 3D ray and the plane cf the face with e􁪽􋵣ch edge of the face. This in turn requires access to the e􁪽􋵤dpolnts of each edge of the face. To calculate reserves for 100 rings using 1000 random points, assu􁪽􋵩ing that rings the