mirror of https://github.com/CGAL/cgal
User manual fixes and improvements
This commit is contained in:
Mael Rouxel-Labbé
parent
6cf03d6a72
commit
f230028a0b
|
|
@ -12,7 +12,7 @@ namespace CGAL {
|
|||
<img src="isosurfacing_teaser.png" style="max-width:50%;"/>
|
||||
</center>
|
||||
\cgalFigureCaptionBegin{IsosurfacingTeaser}
|
||||
Generating a surface from a 3D gray level image using Marching Cubes (3D input image: qim.dk)
|
||||
Generating a surface from a 3D gray level image using Marching Cubes (3D input image from qim.dk)
|
||||
\cgalFigureCaptionEnd
|
||||
|
||||
\section SecIsoSurfacingIntroduction Introduction
|
||||
|
|
@ -24,19 +24,19 @@ the level set forms a surface.
|
|||
In the following, we shall refer to the the field of scalar values as the value field.
|
||||
"Isosurfacing", also known as "isosurface extraction" or "contouring", is the process of constructing
|
||||
the isosurface corresponding to a given value field and isovalue.
|
||||
Isosurfacing is often needed for volume visualization and for the simulation of physical phenomena.
|
||||
%Isosurfacing is often needed for volume visualization and for the simulation of physical phenomena.
|
||||
|
||||
This \cgal package provides methods to extract isosurfaces from 3D value fields.
|
||||
These contouring techniques rely on the partition of the 3D space and of the field to construct
|
||||
an approximate representation of the isosurface.
|
||||
The 3D value field can be described through various representations: an implicit function,
|
||||
an interpolated set of discrete sampling values, etc. (see \ref SecIsosurfacingExamples).
|
||||
an interpolated set of discrete sampling values, a 3D image, etc. (see \ref SecIsosurfacingExamples).
|
||||
The isovalue is user-defined.
|
||||
The output is a polygon soup, made either of triangles or quads depending on the method,
|
||||
and may consist of a single connected component, or multiple, disjoint components.
|
||||
Note that due to the inherent approximate nature of these discrete methods that only sample 3D value fields,
|
||||
parts of the "true" isosurface may be missing from the output, and the output may contain artifacts
|
||||
that re not present in the true isosurface.
|
||||
that are not present in the true isosurface.
|
||||
|
||||
\section SecIsosurfacingMethods Isosurfacing Methods
|
||||
|
||||
|
|
@ -104,6 +104,11 @@ does not intersect the domain boundaries.
|
|||
</center>
|
||||
\cgalFigureCaptionBegin{IsosurfacingMCTMC}
|
||||
Marching Cubes vs Topologically Correct Marching Cubes.
|
||||
Some vertex values can represent complex surfaces within a single cell: on the left,
|
||||
the values at the vertices of the cell have been interpolated within the cell and correspond
|
||||
to a tunnel-like surface. This surface is not correctly recovered when applying the cases of
|
||||
the Marching Cubes algorithm to the cell: 2 independent disk-like sheets are created (middle).
|
||||
However, by inserting new vertices, TMC correctly captures the topology within a single cell (right).
|
||||
\cgalFigureCaptionEnd
|
||||
|
||||
\subsection SubSecDualContouring Dual Contouring (DC)
|
||||
|
|
@ -148,11 +153,13 @@ of the output surface mesh.
|
|||
| ---- | ---- | ---- | ---- | ---- | ---- |
|
||||
MC | Triangles | no | no | no | no |
|
||||
TMC | Triangles | yes | yes | yes | no |
|
||||
DC | Polygons | no | no | no | yes (not guaranteed) |
|
||||
</center>
|
||||
DC | Quads** | no | no | no | yes (not guaranteed) |
|
||||
|
||||
(* assuming the isosurface does not exit the specified bounding box of the input 3D domain)
|
||||
|
||||
(** which can be triangulated on-the-fly)
|
||||
</center>
|
||||
|
||||
Note that the output mesh has boundaries when the isosurface intersects the domain boundaries,
|
||||
regardless of the method (see \cgalFigureRef{IsosurfacingOpen}).
|
||||
|
||||
|
|
@ -170,12 +177,12 @@ Output meshes can have boundaries when the isosurface intersects the domain boun
|
|||
|
||||
The following functions are the main entry points to the isosurfacing algorithms:
|
||||
<ul>
|
||||
<li>Marching Cubes</li>: `CGAL::Isosurfacing::marching_cubes()`, using the named parameter:`use_topologically_correct_marching_cubes` set to `false`;
|
||||
<li>Topologically Correct Marching Cubes</li>: `CGAL::Isosurfacing::marching_cubes()`;
|
||||
<li>Marching Cubes</li>: `CGAL::Isosurfacing::marching_cubes()`, using the named parameter: `use_topologically_correct_marching_cubes` set to `false`;
|
||||
<li>Topologically Correct Marching Cubes</li>: `CGAL::Isosurfacing::marching_cubes()`, using the named parameter: `use_topologically_correct_marching_cubes` set to `true`;
|
||||
<li>%Dual Contouring</li>: `CGAL::Isosurfacing::dual_contouring()`.
|
||||
</ul>
|
||||
|
||||
These three free functions share the same signature:
|
||||
All these free functions share the same signature:
|
||||
|
||||
\code{.cpp}
|
||||
template <typename ConcurrencyTag = CGAL::Sequential_tag,
|
||||
|
|
@ -185,7 +192,8 @@ template <typename ConcurrencyTag = CGAL::Sequential_tag,
|
|||
void ...(const Domain& domain,
|
||||
const typename Domain::FT isovalue,
|
||||
PointRange& points,
|
||||
PolygonRange& polygons);
|
||||
PolygonRange& polygons,
|
||||
...);
|
||||
\endcode
|
||||
|
||||
The input (space partition, value field, gradient field) is provided in the form of a `domain`,
|
||||
|
|
@ -232,7 +240,7 @@ Both these domain models have template parameters enabling the user to customize
|
|||
for `CGAL::Isosurfacing::Marching_cubes_domain_3`, and a dichotomy
|
||||
for `CGAL::Isosurfacing::Dual_contouring_domain_3`. This parameter should
|
||||
be adjusted depending on how the value field is defined: there is for
|
||||
example no point incorporating a dichotomy in Dual Contouring if the value field is defined
|
||||
example no point incorporating a dichotomy in %Dual Contouring if the value field is defined
|
||||
through linear interpolation. Users can pass their own edge intersection
|
||||
oracle, provided it meets the requirements described by the concept
|
||||
`IsosurfacingEdgeIntersectionOracle_3`.
|
||||
|
|
@ -291,12 +299,6 @@ Results of the %Dual Contouring algorithm: untriangulated (left column) or trian
|
|||
unconstrained vertex location (top row) or constrained vertex location (bottom row).
|
||||
\cgalFigureCaptionEnd
|
||||
|
||||
\subsection SubSecDCOctreeExample Dual Contouring using Octree
|
||||
|
||||
The following example shows the use of an octree for dual contouring or marching cubes.
|
||||
|
||||
\cgalExample{Isosurfacing_3/dual_contouring_octree.cpp}
|
||||
|
||||
\subsection SubSecImplicitDataExample Implicit Data
|
||||
|
||||
The following example shows the usage of Marching Cubes and %Dual Contouring algorithms to extract
|
||||
|
|
@ -336,6 +338,15 @@ negative inside the mesh.
|
|||
|
||||
\cgalExample{Isosurfacing_3/contouring_mesh_offset.cpp}
|
||||
|
||||
\subsection SubSecContouringOctreeExample Contouring using Octrees
|
||||
|
||||
The following example shows the use of an octree as discretization instead of a %Cartesian grid
|
||||
for both %Dual Contouring and Marching Cubes. Note that in this configuration, all methods
|
||||
lose guarantees, and cracks can easily appear in the surface if the octree's surface is not
|
||||
correctly constructed.
|
||||
|
||||
\cgalExample{Isosurfacing_3/contouring_octree.cpp}
|
||||
|
||||
\section SecIsosurfacingHistory Design and Implementation History
|
||||
|
||||
The development of this package started during the 2022 Google Summer of Code, with the contribution
|
||||
|
|
|
|||
|
|
@ -5,6 +5,6 @@
|
|||
\example Isosurfacing_3/contouring_mesh_offset.cpp
|
||||
\example Isosurfacing_3/contouring_vtk_image.cpp
|
||||
\example Isosurfacing_3/dual_contouring.cpp
|
||||
\example Isosurfacing_3/dual_contouring_octree.cpp
|
||||
\example Isosurfacing_3/contouring_octree.cpp
|
||||
\example Isosurfacing_3/marching_cubes.cpp
|
||||
*/
|
||||
|
|
|
|||
|
|
@ -48,9 +48,9 @@ auto blobby_function = [](const Point& p) -> FT
|
|||
return std::exp(-1.5 * ((p.x() - 0.2) * (p.x() - 0.2) + (p.y() - 0.2) * (p.y() - 0.2) + (p.z() - 0.2) * (p.z() - 0.2))) +
|
||||
std::exp(-1.5 * ((p.x() + 0.2) * (p.x() + 0.2) + (p.y() + 0.2) * (p.y() + 0.2) + (p.z() + 0.2) * (p.z() + 0.2))) +
|
||||
std::exp(-1.5 * ((p.x() - 0.4) * (p.x() - 0.4) + (p.y() + 0.4) * (p.y() + 0.4) + (p.z() - 0.4) * (p.z() - 0.4))) +
|
||||
std::exp(-6 * ((p.x() - 0.1) * (p.x() - 0.1) + (p.y() - 0.1) * (p.y() - 0.1))) + // Tentacle along z-axis
|
||||
std::exp(-6 * ((p.y() + 0.1) * (p.y() + 0.1) + (p.z() + 0.1) * (p.z() + 0.1))) + // Tentacle along x-axis
|
||||
std::exp(-6 * ((p.x() + 0.1) * (p.x() + 0.1) + (p.z() - 0.1) * (p.z() - 0.1))) - // Tentacle along y-axis
|
||||
std::exp(-6 * ((p.x() - 0.1) * (p.x() - 0.1) + (p.y() - 0.1) * (p.y() - 0.1))) +
|
||||
std::exp(-6 * ((p.y() + 0.1) * (p.y() + 0.1) + (p.z() + 0.1) * (p.z() + 0.1))) +
|
||||
std::exp(-6 * ((p.x() + 0.1) * (p.x() + 0.1) + (p.z() - 0.1) * (p.z() - 0.1))) -
|
||||
0.3;
|
||||
};
|
||||
|
||||
|
|
@ -59,9 +59,9 @@ auto blobby_gradient = [](const Point& p) -> Vector
|
|||
const FT g1 = -3 * std::exp(-1.5 * ((p.x() - 0.2) * (p.x() - 0.2) + (p.y() - 0.2) * (p.y() - 0.2) + (p.z() - 0.2) * (p.z() - 0.2)));
|
||||
const FT g2 = -3 * std::exp(-1.5 * ((p.x() + 0.2) * (p.x() + 0.2) + (p.y() + 0.2) * (p.y() + 0.2) + (p.z() + 0.2) * (p.z() + 0.2)));
|
||||
const FT g3 = -3 * std::exp(-1.5 * ((p.x() - 0.4) * (p.x() - 0.4) + (p.y() + 0.4) * (p.y() + 0.4) + (p.z() - 0.4) * (p.z() - 0.4)));
|
||||
const FT g4 = -12 * std::exp(-6 * ((p.x() - 0.1) * (p.x() - 0.1) + (p.y() - 0.1) * (p.y() - 0.1))); // Gradient for z-axis tentacle
|
||||
const FT g5 = -12 * std::exp(-6 * ((p.y() + 0.1) * (p.y() + 0.1) + (p.z() + 0.1) * (p.z() + 0.1))); // Gradient for x-axis tentacle
|
||||
const FT g6 = -12 * std::exp(-6 * ((p.x() + 0.1) * (p.x() + 0.1) + (p.z() - 0.1) * (p.z() - 0.1))); // Gradient for y-axis tentacle
|
||||
const FT g4 = -12 * std::exp(-6 * ((p.x() - 0.1) * (p.x() - 0.1) + (p.y() - 0.1) * (p.y() - 0.1)));
|
||||
const FT g5 = -12 * std::exp(-6 * ((p.y() + 0.1) * (p.y() + 0.1) + (p.z() + 0.1) * (p.z() + 0.1)));
|
||||
const FT g6 = -12 * std::exp(-6 * ((p.x() + 0.1) * (p.x() + 0.1) + (p.z() - 0.1) * (p.z() - 0.1)));
|
||||
|
||||
return Vector(g1 * (p.x() - 0.2) + g2 * (p.x() + 0.2) + g3 * (p.x() - 0.4) + g4 * (p.x() - 0.1) + g6 * (p.x() + 0.1),
|
||||
g1 * (p.y() - 0.2) + g2 * (p.y() + 0.2) + g3 * (p.y() + 0.4) + g4 * (p.y() - 0.1) + g5 * (p.y() + 0.1),
|
||||
|
|
|
|||
Loading…
Reference in New Issue