magnum/doc/shapes.dox

/*
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namespace Magnum { namespace Shapes {
/** @page shapes Collision detection
@brief Collection of simple shapes for high performance collision detection.

The essential thing in collision detection is to define a complex object with
collection of simple shapes, for which it is easy to detect collisions. These
shapes can be either one-, two- or three-dimensional and they can be grouped
together using various operations.

@tableofcontents

@section shapes-collection Available shapes

%Magnum provides a set of simple shapes for collision detection, similarly to
what is found in many other collision detection libraries. Additionally some
shapes are provided in inverted form -- e.g. inverted box detects collisions on
outside instead of inside, which might be useful for example to create bounds
around platformer game level.

@subsection shapes-1D One-dimensional shapes

- @ref Shapes::Point "Shapes::Point*D" -- @copybrief Shapes::Point
- @ref Shapes::Line "Shapes::Line*D" -- @copybrief Shapes::Line
- @ref Shapes::LineSegment "Shapes::LineSegment*D" -- @copybrief Shapes::LineSegment

Because of numerical instability it's not possible to detect collisions of
line and point. %Collision of two lines can be detected only in 2D.

@subsection shapes-2D Two-dimensional shapes

- Shapes::Plane -- @copybrief Shapes::Plane

@subsection shapes-3D Three-dimensional shapes

- @ref Shapes::Sphere "Shapes::Sphere*D" -- @copybrief Shapes::Sphere
- @ref Shapes::InvertedSphere "Shapes::InvertedSphere*D" -- @copybrief Shapes::InvertedSphere
- @ref Shapes::Cylinder "Shapes::Cylinder*D" -- @copybrief Shapes::Cylinder
- @ref Shapes::Capsule "Shapes::Capsule*D" -- @copybrief Shapes::Capsule
- @ref Shapes::AxisAlignedBox "Shapes::AxisAlignedBox*D" -- @copybrief Shapes::AxisAlignedBox
- @ref Shapes::Box "Shapes::Box*D" -- @copybrief Shapes::Box

The easiest (and most efficient) shape combination for detecting collisions
is point and sphere, followed by two spheres. Computing collision of two boxes
is least efficient.

@section shapes-composition Creating shape compositions

%Shapes can be composed together using one of three available logical
operations: AND, OR and NOT. These operations are mapped to operator&&(),
operator||() and operator!(), so for example creating negation of logical OR
of line segment and point is simple as this:
@code
Shapes::LineSegment3D segment;
Shapes::Point3D point;

Shapes::Composition3D composition = !(segment || point);
@endcode

@note Logical operations are not the same as set operations -- intersection of
    two spheres will not generate any collision if they are disjoint, but
    logical AND will if the object collides with both of them.

@subsection shapes-simplification Providing simplified version of shape for better performance

If there are many shapes composed together, it might hurt performance of
collision detection, because it might be testing collision with more shapes
than necessary. It's then good to specify simplified version of such shape,
so the collision detection is done on the complex one if and only if collision
was detected with the simplified shape. It is in fact logical AND using
operator&&() - the collision is initially detected on first (simplified) shape
and then on the other:
@code
Shapes::Sphere3D sphere;
Shapes::Box3D box;
Shapes::AxisAlignedBox3D simplified;

Shapes::Composition3D composition = simplified && (sphere || box);
@endcode

@section shapes-collisions Detecting shape collisions

%Shape pairs which have collision occurence detection implemented can be tested
for collision using operator%(). The operator returns boolean describing
whether the collision happened or not. Example:
@code
Shapes::Point3D point;
Shapes::Sphere3D sphere;

bool collide = point % sphere;
@endcode

As this is useful for e.g. menu handling and simple particle systems, for
serious physics you often need more information like contact point, separation
normal and penetration depth. For shape pairs which have implemented this
detailed collision detection you can use `operator/()`, which returns @ref Collision
object. Note that unlike with `operator%()` mentioned above, this operation is
not commutative. See @ref Collision class documentation for more information
about the returned data. Example:
@code
Shapes::Collision3D c = point/sphere;
if(c) {
    Vector3 translation = c.separationNormal()*c.separationDistance();
    // translate point by translation...
}
@endcode

@section shapes-scenegraph Integration with scene graph

%Shape can be attached to object in the scene using Shapes::Shape feature and
then used for collision detection. You can also use DebugTools::ShapeRenderer
to visualize the shape for debugging purposes.
@code
Object3D object;
auto shape = Shapes::Shape<Shapes::Sphere3D>(object, {{}, 23.0f});
@endcode

See also @ref scenegraph for introduction.

*/
}}}