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Index.
Miscellaneous terms
This file provides some entries for various keywords that are not
used as name pointers elsewhere for ambiguity, incredible obscurity,
or some other reason.
Alice
A keyword for a special purpose command not documented.
Area
As a keyword, area is a read-only attribute of a facet.
Area_fixed
An obsolete way of declaring the total area of the surface fixed in the
datafile. Synonym: fixed_area. The preferred way of doing this now is to define a fixed
named quantity in the datafile,
such as
quantity the_area fixed = 2.3 global_method facet_area
This permits all the named quantity features to be used.
Attribute
As a keyword, "attribute" is used in the
define command for element
extra attributes.
Bare
As a keyword, "bare" is a
vertex attribute or an
edge attribute set by
the user that tells the Evolver not to expect the vertex or edge to
be attached to a facet.
Body
A body is a three dimensional geometric
element.
As a command keyword, "body" is an element name in
element generators,
either as the main element type, or as a subelement of a facet.
Burchard
A keyword for a special purpose command not documented.
Color
As a keyword, "color" is an attribute of edges and facets.
For the permitted values, see colors.
Conducting_knot_energy
Datafile keyword that automatically creates an energy named quantity
using the method
knot_energy as a global method.
May be followed in the datafile with a modulus value.
Insulating_knot_energy
Datafile keyword that automatically creates an energy named quantity
using the method
uniform_knot_energy as a global method.
May be followed in the datafile with a modulus value.
Constraint
"Constraint" can be used in a
general sense,
but as a keyword it refers to
level set constraints.
"Constraint" and "constraints" are interchangeable.
Content
"Content" is used to mean volume (or area, in the string model)
in constraint integrals.
Convex
A keyword used in declaring a
constraint
in the datafile that causes
a gap energy to be included.
The idea is to prevent straight edges and facets from
short-cutting curved constraints with big gaps.
Density
A keyword referring either to the gravitational density of a body, or
to the surface tension of a facet, or to the linear tension of an edge.
In the latter two cases, "density" is synonymous with "tension".
Edge
In general, one of the basic geometric elements. As a keyword, it
is used in element generators.
Synonym: edges.
Efixed
Obsolete datafile attribute to make an edge fixed without fixing its endpoints.
Keyword retained just for compatibility with old dump files.
Eprint
Function that prints an expression and returns the value. Syntax: eprint expr.
Meant for debugging; probably an archaic leftover from when the command
language was not as developed. Example: print sum(facet, eprint area)
will print out all the facet areas and then the sum.
Facet
>
In general, one of the basic geometric elements. In the soapfilm model,
it is a triangle defined by its three oriented edges. In the string model,
it is a connected sequence of edges of arbitrary number. In the simplex
model, it is a simplex of dimension given by the surface_dimension
item in the top of the datafile, and is defined by its vertices.
Fixed
Attribute that can be applied to
vertices,
edges,
facets, or
named quantities.
Formula
Datafile keyword used in
level set constraints
to introduce the function formula. Synonym: function
Gauss_curvature
Datafile keyword that automatically creates an energy named quantity
using the method
gauss_curvature_integral
as a global method.
May be followed in the datafile with a modulus value.
Tolerance
As a keyword, "tolerance" refers to a
fixed quantity attribute
that is used as the criterion for convergence. Uses
target_tolerance as the
default value.
Div_normal_curvature
Toggle to make sq_mean_curvature energy calculate the mean curvature
by the divergence of the normal vectors at the vertices of a facet.
Force_pos_def
Toggle. If this is on during YSMP factoring of Hessian and the Hessian
turns up indefinite, something will be added to the diagonal element
to make it positive definite. Left over from some experiment probably.
H_inverse_metric
Toggle. Replaces force by Laplacian of force. For doing motion
by Laplacian of mean curvature.
Modulus
A keyword that is an attribute of a
named quantity
or a method instance, which
is a multiplier for the calculated value.
Opacity
Facet attribute for transparency on some geomview systems.
Syntax: set facet opacity value where value
is between 0 and 1. Actually, this just sets a global variable
for all facets simultaneously. The value is passed to geomview in
the alpha slot of the color.
Parameter
Refers to either a
parametric boundary
parameter, or a user-defined variable.
Parameter_file
In the top section of the datafile, a variable can be initialized
with a set of values in a file with the syntax
PARAMETER name PARAMETER_FILE string
I forget exactly how it is all supposed to work.
Pressure
Usually means an attribute of
fixed-volume bodies or
fixed named
quantities that is actually the Lagrange multiplier for the constraint.
As body attribute in the datafile, establishes
fixed pressure for the
body.
Also used rarely in the top section of the datafile to establish the
ideal gas model.
Surface_energy
An obsolete way of including vector surface energy integrals in the
datafile. The present method is to use
a named quantity
with the facet_vector_integral
method.
Total
An obsolete syntax for the value of a named quantity (e.g. my_quant) is
"total my_quant". The present syntax is "my_quant.value".
Valence
An attribute of a vertex, which is the number of incident edges,
or an attribute of an edge, which is the number of incident facets,
or an attribute of a facet, which is the number of edges on the facet.
Vertex
One of the basic geometric elements.
As a keyword, it is used
in element generators.
Utest
Runs a test to see if triangulation is Delaunay. Meant for higher
dimensions and simplex model.
Stability_test
Command to find largest eigenvalue of
mobility matrix. Don't really
recall what this was for.
Tag
An obsolete facet attribute, once used to associate an arbitrary
value with a facet. Now superseded by
extra attributes.
Dynamic load libraries.
This feature hasn't been used much, but documentation is included here
for completeness.
Many Evolver features, such as
level set constraints,
parametric boundaries,
named method integrands, and Riemannian
metrics require user-defined functions of a set of arguments.
The expressions for these functions are ordinarily stored as a parse tree
and interpreted each time needed, which can be much slower that evaluating
compiled expressions. There is a way to use a set of compiled functions
specific to a datafile through a mechanism known as dynamic loading.
Here a library of functions for a datafile is separately compiled,
and then loaded at runtime when a the datafile is loaded. Currently,
the Evolver only implements a dynamic loading mechanism found on
many unix systems, whose presence can be tested by looking for the
existence of the file /usr/include/dlfcn.h. If it exists, you can
enable dynamic loading by including -DENABLE_DLL in the CFLAGS line
in the Makefile. On some systems, you may need to include -ldl on
the GRAPHLIB line also, to link Evolver with functions such as
dlopen().
To create the library for a datafile, write a source file containing
C code for the desired functions, compile it, and link it into a
shared library. The function should be able to compute the value
and the partial derivatives of the function, and its second partials
if you are going to use any Hessian features.
A sample source file for a 2-dimensional datafile:
#define FUNC_VALUE 1
#define FUNC_DERIV 2
#define FUNC_SECOND 3
#define MAXCOORD 4 /* must be same as in Evolver!! */
#define REAL double /* long double if Evolver compiled with -DLONGDOUBLE */
struct dstack { REAL value;
REAL deriv[2*MAXCOORD];
REAL second[2*MAXCOORD][2*MAXCOORD]; };
void func1 ( mode, x, s )
int mode; /* FUNC_VALUE, FUNC_DERIV, FUNC_SECOND */
REAL *x; /* pointer to list of arguments */
struct dstack *s; /* for return values */
{ REAL value;
s->value = x[0] + x[1]*x[1];
if ( mode == FUNC_VALUE ) return;
/* first partials */
s->deriv[0] = 1.0;
s->deriv[1] = 2*x[1];
if ( mode == FUNC_DERIV ) return;
/* second partials */
s->second[0][0] = 0.0;
s->second[0][1] = 0.0;
s->second[1][0] = 0.0;
s->second[1][1] = 2.0;
return;
}
Supposing the sourcefile name to be foo.c,
compile and link on SGI systems (IRIX 5.0.1 or above) with
cc -c foo.c
ld -shared foo.o -o foo.so
Sun systems are the same, but with -s in place of -shared. For
other systems, consult the ld documentation for the option to
make a shared library or dynamic load library.
To use the functions in a datafile, include a line at the top
of the datafile before any of the functions are used:
load_library "foo.so"
The current directory and the EVOLVERPATH
will be searched for the library.
Up to 10 libraries may be loaded.
Afterwards, any of the functions may be invoked just by using
their name, without an explicit argument list because the argument
list is always implicit where these functions are legal. Examples,
supposing func2 is also defined with one argument:
constraint 1
formula: func1
boundary 1 parameters 2
x1: func2
x2: 3*func2 + sin(p1)
It is up to you to make sure the number of arguments your function
expects is the same as the number implicit in the use of the function.
You do not need to explicitly declare your functions in the datafile.
Any undefined identifier is checked to see if it is a dynamically
loaded function.
NOTE: This implementation of dynamic loading is experimental, and the
interface described here may change in the future.
__bhead_index
A body attribute used internally by Hessian routines.
__vhead_index
A vertex attribute used internally by Hessian routines.
form_factors
A facet extra attribute vector used by several elastic energy named
methods: linear_elastic,
neo_hookean,
relaxed_elastic,
relaxed_elastic_A,
SVK_elastic, and
dirichlet_elastic.
The entries are the dot products of
the sides of the relaxed facet. Due to symmetry, there are only three
distinct dot products, so form_factors just has length 3. The entries
are {s11,s12,s22}, where s11 = dot(v2-v1,v2-v1), s12 = dot(v2-v1,v3-v1),
and s22 = dot(v3-v1,v3-v1). If form_factor is not defined by the user,
it will be created by Evolver, and the initial facet shape will be assumed
to be unstrained.
poisson_ratio
Facet extra attribute used by various elastic named methods:
linear_elastic,
linear_elastic_B,
neo_hookean,
relaxed_elastic,
relaxed_elastic_A,
SVK_elastic, and
dirichlet_elastic.
This is the two-dimensional isotropic poisson ratio.
Some physical surfaces have their lowest energy state when their
mean curvature is some nonzero value. An example is a membrane
made of parallel stacked molecules which have one end bigger than
the other. Their curvature energy is thus proportional to (h-h0)^2,
where h is the actual mean curvature and h0 is the equilibrium or
intrinsic mean curvature. Several of the squared mean curvature
named methods can use h0, either in the form of a variable h_zero
or a real-valued vertex attribute h_zero. If the vertex attribute
exists, it takes precedence.
Methods using h_zero:
Methods not using h_zero:
knot_power
Internal read-write variable used as exponent on some term in
various knot energies. Named methods using knot_power are:
surface_knot_power
Internal read-write variable used in the
facet_knot_energy and
sphere_knot_energy
named methods
as the exponent of the denominator.
LEBweight>
Facet extra attribute used to weight individual facets in the
named methods linear_elastic_B,
named methods relaxed_elastic,
named methods relaxed_elastic_A,
old_force_ribiere
Vertex extra attribute used internally by conjugate gradient mode.
parameter_1
A generic parameter used by a couple of named methods.
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Index.