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```    1 BRL-CAD Boundary-Representation Primitive
2 -----------------------------------------
3
4 -- Introduction --
5
6 This document describes the new Boundary-representation (BREP)
7 primitive that has been implemented in BRL-CAD for use with external
8 geometry import and improved visualisation.
9
10 The primitive is not yet complete, and is currently quite buggy, so
11 this document also serves to describe the current state of
12 development, and the knowledge a developer needs to continue working
13 on this primitive.
14
15
16 -- BREP Description --
17
18 A boundary-representation is a method of representing solid geometry
19 by describing its topology and corresponding geometry. In other words,
20 the vertexes, edges, and faces as well as the points, curves, and
21 surfaces belonging to those topological elements.
22
23 For example, a cube has 8 vertexes each mapping to 1 point in space, 6
24 faces each mapping to 1 surface, and 8 edges each shared by two faces
25 and sharing its two vertexes with two other faces and owning 1 real
26 curve.
27
28 Actually creating/using a BREP requires keeping track of a lot of details,
29 including everything mentioned above, plus curve / face orientations
30 (a CCW edge/vertex ordering is usually used for determining front/back
31 designations.)
32
34 geometry) primitive/library.
35
36 [[describe reasons for not using the existing library]]
37
38 One can use many types of surface and curve geometry, but generally a
39 small subset are used by any particular implementation: e.g. having
40 converted a few pieces of Pro/E through IGES to the new BRL-CAD BREP
41 primitive, I've seen the following curve and surface types used:
42
43 * Line
44 * Arc
45 * NURBS curve
46 * Surface of revolution
47 * NURBS surface
48
49 The simple IGES converter used to import and test new geometry handles
50 those types already. Other limitations of the converter are described
51 later in the document.
52
53
54 -- Primitive Implementation --
55
56 openNURBS was chosen to represent the geometry within BRL-CAD. This
57 turned out to be a good and bad choice at the same time:
58
59 * contains a lot of solid functionality
60 * missing a lot of useful and important functionality
61
62 In other words, the openNURBS API provided methods of functions for
63 several pieces of functionality that had implementations removed when
64 McNeil and Associates released openNURBS as essentially public domain
65 code. This slowed development somewhat and meant the functionality had
66 to be reimplemented by hand.
67
68 The API is relatively straightforward C++, and it is used to evaluate
69 geometry and represent/store BREPs in the BRL-CAD geometry file,
70 through the built-in serialization facility (i.e. 3DM files).
71
72
73 -- Raytracing BREPs --
74
75 See Abert et al. (raytracing 06 paper: Direct and Fast Ray Tracing of NURBS
76 Surfaces).
77
78 We use a two-dimensional root-finding technique: we represent the ray
79 as two orthogonal planes (the intersection of the planes includes the
80 ray), and then find the root of an equation that represents the
81 gradient of the distance from the point to the intersection of the ray
82 planes. When this gradient becomes zero (we found a root), we've also
83 found the uv parameters for the intersection point.
84
85 Newton iteration is used, mostly since it is simple, displays
86 quadratic convergence when using good guesses, and is amenable to
87 acceleration using SIMD instructions.
88
89 Evaluation of the surface and its derivatives is done by the openNURBS
90 library at this point. The Abert paper gives some information on how
91 to do the evaluation using SIMD instructions (needed for speeding
92 things up).
93
94 A simple SIMD vector class has been implemented (see vector.h)
95 supporting both SSE2 and FPU vector operations. This is currently only
96 lightly used, since no optimization work has taken place yet
97 (correctness before optimization).
98
99 After intersection, we need to trim the surface. Every edge of a BREP
100 is part of a loop "within" a face. Loops define boundaries on
101 faces. In our cube example above, the four edges of a each face
102 comprise a single loop (in this case an outer boundary). The surface
103 may be defined as an infinite plane, but this outer boundary loop
104 limits it to the area enclosed within those edges. As you may imagine,
105 a face may have more than one loop and these additional loops will
106 always be internal. All loops can also be considered trims, although
107 this term seems to be reserved for actual geometric curves that are
108 parameterized within the domain of an individual surface.
109
110 Properly ray tracing a BREP is difficult (thus, the obvious
111 explanation why this primitive is incomplete). There are several facts
112 about BREPs that result in problematic situations during ray tracing:
113 BREPs are not like implicit solid geometry: there is no nice equation
114 to simply solve (a lot of numerical techniques are used); surfaces,
115 curves and point geometry may not be aligned; there can be gaps
116 between two mated surfaces... and the list goes on.
117
118 Since it's possible to miss a surface but *need* a hit (i.e. it hit an
119 edge but passed between surfaces that did not mate up or overlap), we
120 need to do edge checks: at some point, we find out how far an
121 intersection point or a ray is from some set of edges
122
123
124 -- Current Capabilities & Limitations --
125
126 Developing a BRL-CAD primitive requires a minimum of 4 basic
127 capabilities: reading from a geom db, writing to a geom db, providing
128 a plot of the primitive (for MGED display), and handling shot
129 intersection, which involves finding all intersections with the
130 primitive and returning the results as a list of "segments" (these
131 segments will later be used by BRL-CAD to do its boolean weaving).
132
133 This primitive currently handles the first 3 capabilities fine, but
134 has problems with the intersections (the most important part!)
135
136 Issues:
137
138 * bad acne (possibly caused by missing surfaces? duplicate
139   intersections (making an odd number of hits along the ray), trimming
140   errors?
141
142 * problems with trimming (not completely sure the bezier clipping is
143   correct)
144
145 * possible problems with tolerances (been working with a very small
146   (~2mm) object that has a moderate number of faces/edges)
147
148 * no optimization, bad algorithms: bounding boxes (subsurface bounding
149   boxes) should contain correct metadata concerning the need for
150   trimming within the box, also a list of edges touched by the box for
151   more efficient edge checking, evaluation optimization, etc...
152
153
154 The current issue seems to be that we're missing surfaces altogether or
155 getting extra intersections! or something funky is happening during
156 trimming and edge checking. (BTW Pro/E seems to output overlapping
157 surfaces, relying on the outer boundary loop to trim it - this implies
158 that it should be quite difficult to actually miss both surfaces at an
159 edge (since would have to get at least one intersection if they
160 overlap at the edge!)
161
162 [[ some pictures may be useful here ]]
163
164 See all instances of "XXX" in the code (some may be out of date, but
165 if something was fishy or I was being stupid/lazy/ignorant or some
166 other bit of code was causing a problem, I tried to mark it with XXX.
167
168
169 -- Conceptual/Implementation Issues --
170
171 model-space curve pullback to surface domain for trimming (introduces
172 possible errors while trimming (i.e. at an edge it's possible both
173 surfaces can be trimmed because of inaccuracies of sampling)...
174
175 multiple intersections found
176
177 handling edge/surface grazing consistently
178
179 bezier conversion of nurbs curves for trimming
180
181 subsurface bounding boxes: when subdividing a surface domain and
182 testing for flatness, hard to create a perfect bounding box around the
183 subdomain (i.e. such that all points on the surface lie within the
184 bounding box.) For the most part this may not be a problem, but
185 oblique shots cause problems here (an image would help). Either way,
186 the problem of better fitting bounding boxes (without just arbitrarily
187 increasing the size which would seriously affect performance) needs to
188 be considered... currently attempting to sample an additional 5 points
189 (instead of just the corners). This should serve to handle the current
190 problem.
191
192 Close-up axis aligned rendering of a cylinder from the circular ends
193 produces a halo of spurious points. Ugh!
194
195 Optimize for small objects (there are some fixed size adjustments in
196 the bounding box/subsurface code).
197
198
199 -- IGES converter --
200
201 A significant bit of time was spent writing the skeleton for a new
202 IGES converter in order to get non-trivial BREP geometry from an
203 external package into BRL-CAD for testing purposes (have been using
204 the piston head part from one of the Pro/E tutorial models).
205
206 I believe this converter can be made production-ready with some work:
207
208 * polish options for output
209
210 * handle assemblies and their proper mapping to BRL-CAD
211
212 * handle naming? (don't know if IGES carries names, or if Pro/E adds
213   them)
214
215 * handle units properly!
216
217 * tolerances when converting are still flaky (fix it) (cause BREP
218   validity problems). Trims endpoint are not within zero tolerance
219   (1e-12), so they "don't match" but they are very very close
220   (1e-11)... so need to go through and call ON_Brep::CloseTrimGap() on
221   each pair of trims in a loop.
222
223 * Run lots of test cases!!!
```