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voro++.hh
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1 // Voro++, a 3D cell-based Voronoi library
2 //
3 // Author : Chris H. Rycroft (LBL / UC Berkeley)
4 // Email : chr@alum.mit.edu
5 // Date : August 30th 2011
6
7 /** \file voro++.hh
8 * \brief A file that loads all of the Voro++ header files. */
9
10 /** \mainpage Voro++ class reference manual
11 * \section intro Introduction
12 * Voro++ is a software library for carrying out three-dimensional computations
13 * of the Voronoi tessellation. A distinguishing feature of the Voro++ library
14 * is that it carries out cell-based calculations, computing the Voronoi cell
15 * for each particle individually, rather than computing the Voronoi
16 * tessellation as a global network of vertices and edges. It is particularly
17 * well-suited for applications that rely on cell-based statistics, where
18 * features of Voronoi cells (eg. volume, centroid, number of faces) can be
19 * used to analyze a system of particles.
20 *
21 * Voro++ is written in C++ and can be built as a static library that can be
22 * linked to. This manual provides a reference for every function in the class
23 * structure. For a general overview of the program, see the Voro++ website at
24 * http://math.lbl.gov/voro++/ and in particular the example programs at
25 * http://math.lbl.gov/voro++/examples/ that demonstrate many of the library's
26 * features.
27 *
28 * \section class C++ class structure
29 * The code is structured around several C++ classes. The voronoicell_base
30 * class contains all of the routines for constructing a single Voronoi cell.
31 * It represents the cell as a collection of vertices that are connected by
32 * edges, and there are routines for initializing, making, and outputting the
33 * cell. The voronoicell_base class form the base of the voronoicell and
34 * voronoicell_neighbor classes, which add specialized routines depending on
35 * whether neighboring particle ID information for each face must be tracked or
36 * not. Collectively, these classes are referred to as "voronoicell classes"
37 * within the documentation.
38 *
39 * There is a hierarchy of classes that represent three-dimensional particle
40 * systems. All of these are derived from the voro_base class, which contains
41 * constants that divide a three-dimensional system into a rectangular grid of
42 * equally-sized rectangular blocks; this grid is used for computational
43 * efficiency during the Voronoi calculations.
44 *
45 * The container_base, container, and container_poly are then derived from the
46 * voro_base class to represent a particle system in a specific
47 * three-dimensional rectangular box using both periodic and non-periodic
48 * boundary conditions. In addition, the container_periodic_base,
49 * container_periodic, and container_periodic_poly classes represent
50 * a particle system in a three-dimensional non-orthogonal periodic domain,
51 * defined by three periodicity vectors that represent a parallelepiped.
52 * Collectively, these classes are referred to as "container classes" within
53 * the documentation.
54 *
55 * The voro_compute template encapsulates all of the routines for computing
56 * Voronoi cells. Each container class has a voro_compute template within
57 * it, that accesses the container's particle system, and computes the Voronoi
58 * cells.
59 *
60 * There are several wall classes that can be used to apply certain boundary
61 * conditions using additional plane cuts during the Voronoi cell compution.
62 * The code also contains a number of small loop classes, c_loop_all,
63 * c_loop_subset, c_loop_all_periodic, and c_loop_order that can be used to
64 * iterate over a certain subset of particles in a container. The latter class
65 * makes use of a special particle_order class that stores a specific order of
66 * particles within the container. The library also contains the classes
67 * pre_container_base, pre_container, and pre_container_poly, that can be used
68 * as temporary storage when importing data of unknown size.
69 *
70 * \section voronoicell The voronoicell classes
71 * The voronoicell class represents a single Voronoi cell as a convex
72 * polyhedron, with a set of vertices that are connected by edges. The class
73 * contains a variety of functions that can be used to compute and output the
74 * Voronoi cell corresponding to a particular particle. The command init()
75 * can be used to initialize a cell as a large rectangular box. The Voronoi cell
76 * can then be computed by repeatedly cutting it with planes that correspond to
77 * the perpendicular bisectors between that particle and its neighbors.
78 *
79 * This is achieved by using the plane() routine, which will recompute the
80 * cell's vertices and edges after cutting it with a single plane. This is the
81 * key routine in voronoicell class. It begins by exploiting the convexity
82 * of the underlying cell, tracing between edges to work out if the cell
83 * intersects the cutting plane. If it does not intersect, then the routine
84 * immediately exits. Otherwise, it finds an edge or vertex that intersects
85 * the plane, and from there, traces out a new face on the cell, recomputing
86 * the edge and vertex structure accordingly.
87 *
88 * Once the cell is computed, there are many routines for computing features of
89 * the the Voronoi cell, such as its volume, surface area, or centroid. There
90 * are also many routines for outputting features of the Voronoi cell, or
91 * writing its shape in formats that can be read by Gnuplot or POV-Ray.
92 *
93 * \subsection internal Internal data representation
94 * The voronoicell class has a public member p representing the
95 * number of vertices. The polyhedral structure of the cell is stored
96 * in the following arrays:
97 *
98 * - pts: a one-dimensional array of floating point numbers, that represent the
99 * position vectors x_0, x_1, ..., x_{p-1} of the polyhedron vertices.
100 * - nu: the order of each vertex n_0, n_1, ..., n_{p-1}, corresponding to
101 * the number of other vertices to which each is connected.
102 * - ed: a two-dimensional table of edges and relations. For the ith vertex,
103 * ed[i] has 2n_i+1 elements. The first n_i elements are the edges e(j,i),
104 * where e(j,i) is the jth neighbor of vertex i. The edges are ordered
105 * according to a right-hand rule with respect to an outward-pointing normal.
106 * The next n_i elements are the relations l(j,i) which satisfy the property
107 * e(l(j,i),e(j,i)) = i. The final element of the ed[i] list is a back
108 * pointer used in memory allocation.
109 *
110 * In a very large number of cases, the values of n_i will be 3. This is because
111 * the only way that a higher-order vertex can be created in the plane()
112 * routine is if the cutting plane perfectly intersects an existing vertex. For
113 * random particle arrangements with position vectors specified to double
114 * precision this should happen very rarely. A preliminary version of this code
115 * was quite successful with only making use of vertices of order 3. However,
116 * when calculating millions of cells, it was found that this approach is not
117 * robust, since a single floating point error can invalidate the computation.
118 * This can also be a problem for cases featuring crystalline arrangements of
119 * particles where the corresponding Voronoi cells may have high-order vertices
120 * by construction.
121 *
122 * Because of this, Voro++ takes the approach that it if an existing vertex is
123 * within a small numerical tolerance of the cutting plane, it is treated as
124 * being exactly on the plane, and the polyhedral topology is recomputed
125 * accordingly. However, while this improves robustness, it also adds the
126 * complexity that n_i may no longer always be 3. This causes memory management
127 * to be significantly more complicated, as different vertices require a
128 * different number of elements in the ed[][] array. To accommodate this, the
129 * voronoicell class allocated edge memory in a different array called mep[][],
130 * in such a way that all vertices of order k are held in mep[k]. If vertex
131 * i has order k, then ed[i] points to memory within mep[k]. The array ed[][]
132 * is never directly initialized as a two-dimensional array itself, but points
133 * at allocations within mep[][]. To the user, it appears as though each row of
134 * ed[][] has a different number of elements. When vertices are added or
135 * deleted, care must be taken to reorder and reassign elements in these
136 * arrays.
137 *
138 * During the plane() routine, the code traces around the vertices of the cell,
139 * and adds new vertices along edges which intersect the cutting plane to
140 * create a new face. The values of l(j,i) are used in this computation, as
141 * when the code is traversing from one vertex on the cell to another, this
142 * information allows the code to immediately work out which edge of a vertex
143 * points back to the one it came from. As new vertices are created, the l(j,i)
144 * are also updated to ensure consistency. To ensure robustness, the plane
145 * cutting algorithm should work with any possible combination of vertices
146 * which are inside, outside, or exactly on the cutting plane.
147 *
148 * Vertices exactly on the cutting plane create some additional computational
149 * difficulties. If there are two marginal vertices connected by an existing
150 * edge, then it would be possible for duplicate edges to be created between
151 * those two vertices, if the plane routine traces along both sides of this
152 * edge while constructing the new face. The code recognizes these cases and
153 * prevents the double edge from being formed. Another possibility is the
154 * formation of vertices of order two or one. At the end of the plane cutting
155 * routine, the code checks to see if any of these are present, removing the
156 * order one vertices by just deleting them, and removing the order two
157 * vertices by connecting the two neighbors of each vertex together. It is
158 * possible that the removal of a single low-order vertex could result in the
159 * creation of additional low-order vertices, so the process is applied
160 * recursively until no more are left.
161 *
162 * \section container The container classes
163 * There are four container classes available for general usage: container,
164 * container_poly, container_periodic, and container_periodic_poly. Each of
165 * these represent a system of particles in a specific three-dimensional
166 * geometry. They contain routines for importing particles from a text file,
167 * and adding particles individually. They also contain a large number of
168 * analyzing and outputting the particle system. Internally, the routines that
169 * compute Voronoi cells do so by making use of the voro_compute template.
170 * Each container class contains routines that tell the voro_compute template
171 * about the specific geometry of this container.
172 *
173 * \section voro_compute The voro_compute template
174 * The voro_compute template encapsulates the routines for carrying out the
175 * Voronoi cell computations. It contains data structures suchs as a mask and a
176 * queue that are used in the computations. The voro_compute template is
177 * associated with a specific container class, and during the computation, it
178 * calls routines in the container class to access the particle positions that
179 * are stored there.
180 *
181 * The key routine in this class is compute_cell(), which makes use of a
182 * voronoicell class to construct a Voronoi cell for a specific particle in the
183 * container. The basic approach that this function takes is to repeatedly cut
184 * the Voronoi cell by planes corresponding neighboring particles, and stop
185 * when it recognizes that all the remaining particles in the container are too
186 * far away to possibly influence cell's shape. The code makes use of two
187 * possible methods for working out when a cell computation is complete:
188 *
189 * - Radius test: if the maximum distance of a Voronoi cell
190 * vertex from the cell center is R, then no particles more than a distance
191 * 2R away can possibly influence the cell. This a very fast computation to
192 * do, but it has no directionality: if the cell extends a long way in one
193 * direction then particles a long distance in other directions will still
194 * need to be tested.
195 * - Region test: it is possible to test whether a specific region can
196 * possibly influence the cell by applying a series of plane tests at the
197 * point on the region which is closest to the Voronoi cell center. This is a
198 * slower computation to do, but it has directionality.
199 *
200 * Another useful observation is that the regions that need to be tested are
201 * simply connected, meaning that if a particular region does not need to be
202 * tested, then neighboring regions which are further away do not need to be
203 * tested.
204 *
205 * For maximum efficiency, it was found that a hybrid approach making use of
206 * both of the above tests worked well in practice. Radius tests work well for
207 * the first few blocks, but switching to region tests after then prevent the
208 * code from becoming extremely slow, due to testing over very large spherical
209 * shells of particles. The compute_cell() routine therefore takes the
210 * following approach:
211 *
212 * - Initialize the voronoicell class to fill the entire computational domain.
213 * - Cut the cell by any wall objects that have been added to the container.
214 * - Apply plane cuts to the cell corresponding to the other particles which
215 * are within the current particle's region.
216 * - Test over a pre-computed worklist of neighboring regions, that have been
217 * ordered according to the minimum distance away from the particle's
218 * position. Apply radius tests after every few regions to see if the
219 * calculation can terminate.
220 * - If the code reaches the end of the worklist, add all the neighboring
221 * regions to a new list.
222 * - Carry out a region test on the first item of the list. If the region needs
223 * to be tested, apply the plane() routine for all of its particles, and then
224 * add any neighboring regions to the end of the list that need to be tested.
225 * Continue until the list has no elements left.
226 *
227 * The compute_cell() routine forms the basis of many other routines, such as
228 * store_cell_volumes() and draw_cells_gnuplot() that can be used to calculate
229 * and draw the cells in a container.
230 *
231 * \section walls Wall computation
232 * Wall computations are handled by making use of a pure virtual wall class.
233 * Specific wall types are derived from this class, and require the
234 * specification of two routines: point_inside() that tests to see if a point
235 * is inside a wall or not, and cut_cell() that cuts a cell according to the
236 * wall's position. The walls can be added to the container using the
237 * add_wall() command, and these are called each time a compute_cell() command
238 * is carried out. At present, wall types for planes, spheres, cylinders, and
239 * cones are provided, although custom walls can be added by creating new
240 * classes derived from the pure virtual class. Currently all wall types
241 * approximate the wall surface with a single plane, which produces some small
242 * errors, but generally gives good results for dense particle packings in
243 * direct contact with a wall surface. It would be possible to create more
244 * accurate walls by making cut_cell() routines that approximate the curved
245 * surface with multiple plane cuts.
246 *
247 * The wall objects can used for periodic calculations, although to obtain
248 * valid results, the walls should also be periodic as well. For example, in a
249 * domain that is periodic in the x direction, a cylinder aligned along the x
250 * axis could be added. At present, the interior of all wall objects are convex
251 * domains, and consequently any superposition of them will be a convex domain
252 * also. Carrying out computations in non-convex domains poses some problems,
253 * since this could theoretically lead to non-convex Voronoi cells, which the
254 * internal data representation of the voronoicell class does not support. For
255 * non-convex cases where the wall surfaces feature just a small amount of
256 * negative curvature (eg. a torus) approximating the curved surface with a
257 * single plane cut may give an acceptable level of accuracy. For non-convex
258 * cases that feature internal angles, the best strategy may be to decompose
259 * the domain into several convex subdomains, carry out a calculation in each,
260 * and then add the results together. The voronoicell class cannot be easily
261 * modified to handle non-convex cells as this would fundamentally alter the
262 * algorithms that it uses, and cases could arise where a single plane cut
263 * could create several new faces as opposed to just one.
264 *
265 * \section loops Loop classes
266 * The container classes have a number of simple routines for calculating
267 * Voronoi cells for all particles within them. However, in some situations it
268 * is desirable to iterate over a specific subset of particles. This can be
269 * achieved with the c_loop classes that are all derived from the c_loop_base
270 * class. Each class can iterate over a specific subset of particles in a
271 * container. There are three loop classes for use with the container and
272 * container_poly classes:
273 *
274 * - c_loop_all will loop over all of the particles in a container.
275 * - c_loop_subset will loop over a subset of particles in a container that lie
276 * within some geometrical region. It can loop over particles in a
277 * rectangular box, particles in a sphere, or particles that lie within
278 * specific internal computational blocks.
279 * - c_loop_order will loop over a specific list of particles that were
280 * previously stored in a particle_order class.
281 *
282 * Several of the key routines within the container classes (such as
283 * draw_cells_gnuplot and print_custom) have versions where they can be passed
284 * a loop class to use. Loop classes can also be used directly and there are
285 * some examples on the library website that demonstrate this. It is also
286 * possible to write custom loop classes.
287 *
288 * In addition to the loop classes mentioned above, there is also a
289 * c_loop_all_periodic class, that is specifically for use with the
290 * container_periodic and container_periodic_poly classes. Since the data
291 * structures of these containers differ considerably, it requires a different
292 * loop class that is not interoperable with the others.
293 *
294 * \section pre_container The pre_container classes
295 * Voro++ makes use of internal computational grid of blocks that are used to
296 * configure the code for maximum efficiency. As discussed on the library
297 * website, the best performance is achieved for around 5 particles per block,
298 * with anything in the range from 3 to 12 giving good performance. Usually
299 * the size of the grid can be chosen by ensuring that the number of blocks is
300 * equal to the number of particles divided by 5.
301 *
302 * However, this can be difficult to choose in cases when the number of
303 * particles is not known a priori, and in thes cases the pre_container classes
304 * can be used. They can import an arbitrary number of particle positions from
305 * a file, dynamically allocating memory in chunks as necessary. Once particles
306 * are imported, they can guess an optimal block arrangement to use for the
307 * container class, and then transfer the particles to the container. By
308 * default, this procedure is used by the command-line utility to enable it to
309 * work well with arbitrary sizes of input data.
310 *
311 * The pre_container class can be used when no particle radius information is
312 * available, and the pre_container_poly class can be used when radius
313 * information is available. At present, the pre_container classes can only be
314 * used with the container and container_poly classes. They do not support
315 * the container_periodic and container_periodic_poly classes. */
316
317 #ifndef VOROPP_HH
318 #define VOROPP_HH
319
320 #include "config.hh"
321 #include "common.hh"
322 #include "cell.hh"
323 #include "v_base.hh"
324 #include "rad_option.hh"
325 #include "container.hh"
326 #include "unitcell.hh"
327 #include "container_prd.hh"
328 #include "pre_container.hh"
329 #include "v_compute.hh"
330 #include "c_loops.hh"
331 #include "wall.hh"
332
333 #endif
rad_option.hh
Header file for the classes encapsulating functionality for the regular and radical Voronoi tessellat...
wall.hh
Header file for the derived wall classes.
c_loops.hh
Header file for the loop classes.
cell.hh
Header file for the voronoicell and related classes.
config.hh
Master configuration file for setting various compile-time options.
v_compute.hh
Header file for the voro_compute template and related classes.
unitcell.hh
Header file for the unitcell class.
container_prd.hh
Header file for the container_periodic_base and related classes.
container.hh
Header file for the container_base and related classes.
pre_container.hh
Header file for the pre_container and related classes.
v_base.hh
Header file for the base Voronoi container class.
common.hh
Header file for the small helper functions.