// This file contains the detail API documentation for
// elements defined in the Recast.h.

/**

@defgroup recast Recast

Members in this module are used to create mesh data that is then
used to create Detour navigation meshes.

The are a large number of possible ways to building navigation mesh data.
One of the simple piplines is as follows:

-# Prepare the input triangle mesh.
-# Build a #rcHeightfield.
-# Build a #rcCompactHeightfield.
-# Build a #rcContourSet.
-# Build a #rcPolyMesh.
-# Build a #rcPolyMeshDetail.
-# Use the rcPolyMesh and rcPolyMeshDetail to build a Detour navigation mesh
   tile.

The general life-cycle of the main classes is as follows:

-# Allocate the object using the Recast allocator. (E.g. #rcAllocHeightfield)
-# Initialize or build the object. (E.g. #rcCreateHeightfield)
-# Update the object as needed. (E.g. #rcRasterizeTriangles)
-# Use the object as part of the pipeline.
-# Free the object using the Recast allocator. (E.g. #rcFreeHeightField)

@struct rcConfig
@par

The is a convenience structure that represents an aggregation of parameters 
used at different stages in the Recast build process. Some 
values are derived during the build process. Not all parameters 
are used for all build processes.

Units are usually in voxels (vx) or world units (wu).  The units for voxels, 
grid size, and cell size are all based on the values of #cs and #ch.

In this documentation, the term 'field' refers to heightfield and
contour data structures that define spacial information using an integer
grid.

The upper and lower limits for the various parameters often depend on 
the platform's floating point accuraccy as well as interdependencies between 
the values of multiple parameters.  See the individual parameter 
documentation for details.

@note First you should decide the size of your agent's logical cylinder. 
If your game world uses meters as units, a reasonable starting point for 
a human-sized agent might be a radius of `0.4` and a height of `2.0`.

@var rcConfig::borderSize
@par

This value represents the the closest the walkable area of the heightfield 
should come to the xz-plane AABB of the field. It does not have any
impact on the borders around internal obstructions.

@var rcConfig::tileSize
@par

This field is only used when building multi-tile meshes.

@var rcConfig::cs
@par

The voxelization cell size #cs defines the voxel size along both axes of 
the ground plane: x and z in Recast. This value is usually derived from the 
character radius `r`. A recommended starting value for #cs is either `r/2` 
or `r/3`. Smaller values of #cs will increase rasterization resolution and 
navmesh detail, but total generation time will increase exponentially.  In 
outdoor environments, `r/2` is often good enough.  For indoor scenes with 
tight spaces you might want the extra precision, so a value of `r/3` or 
smaller may give better results.

The initial instinct is to reduce this value to something very close to zero 
to maximize the detail of the generated navmesh. This quickly becomes a case 
of diminishing returns, however. Beyond a certain point there's usually not 
much perceptable difference in the generated navmesh, but huge increases in 
generation time.  This hinders your ability to quickly iterate on level 
designs and provides little benefit.  The general recommendation here is to 
use as large a value for #cs as you can get away with.

#cs and #ch define voxel/grid/cell size.  So their values have significant 
side effects on all parameters defined in voxel units.

The minimum value for this parameter depends on the platform's floating point 
accuracy, with the practical minimum usually around 0.05.

@var rcConfig::ch
@par

The voxelization cell height #ch is defined separately in order to allow for 
greater precision in height tests. A good starting point for #ch is half the 
#cs value. Smaller #ch values ensure that the navmesh properly connects areas 
that are only separated by a small curb or ditch.  If small holes are generated 
in your navmesh around where there are discontinuities in height (for example, 
stairs or curbs), you may want to decrease the cell height value to increase 
the vertical rasterization precision of Recast.

#cs and #ch define voxel/grid/cell size.  So their values have significant 
side effects on all parameters defined in voxel units.

The minimum value for this parameter depends on the platform's floating point 
accuracy, with the practical minimum usually around 0.05.

@var rcConfig::walkableSlopeAngle
@par

The parameter #walkableSlopeAngle is to filter out areas of the world where 
the ground slope would be too steep for an agent to traverse. This value is 
defined as a maximum angle in degrees that the surface normal of a polgyon 
can differ from the world's up vector.  This value must be within the range 
`[0, 90]`.

The practical upper limit for this parameter is usually around 85 degrees.

@var rcConfig::walkableHeight
@par

This value defines the worldspace height `h` of the agent in voxels. Th value 
of #walkableHeight should be calculated as `ceil(h / ch)`.  Note this is based 
on #ch not #cs since it's a height value.

Permits detection of overhangs in the source geometry that make the geometry
below un-walkable. The value is usually set to the maximum agent height.

@var rcConfig::walkableClimb
@par

The #walkableClimb value defines the maximum height of ledges and steps that 
the agent can walk up. Given a designer-defined `maxClimb` distance in world 
units, the value of #walkableClimb should be calculated as `ceil(maxClimb / ch)`.  
Note that this is using #ch not #cs because it's a height-based value.

Allows the mesh to flow over low lying obstructions such as curbs and 
up/down stairways. The value is usually set to how far up/down an agent can step.

@var rcConfig::walkableRadius
@par

The parameter #walkableRadius defines the worldspace agent radius `r` in voxels.  
Most often, this value of #walkableRadius should be calculated as `ceil(r / cs)`. 
Note this is based on #cs since the agent radius is always parallel to the ground 
plane.

If the #walkableRadius value is greater than zero, the edges of the navmesh will 
be pushed away from all obstacles by this amount.

A non-zero #walkableRadius allows for much simpler runtime navmesh collision checks.
The game only needs to check that the center point of the agent is contained within 
a navmesh polygon.  Without this erosion, runtime navigation checks need to collide
the geometric projection of the agent's logical cylinder onto the navmesh with the 
boundary edges of the navmesh polygons.

In general, this is the closest any part of the final mesh should get to an 
obstruction in the source geometry.  It is usually set to the maximum
agent radius.

If you want to have tight-fitting navmesh, or want to reuse the same navmesh for 
multiple agents with differing radii, you can use a `walkableRadius` value of zero.
Be advised though that you will need to perform your own collisions with the navmesh
edges, and odd edge cases issues in the mesh generation can potentially occur.  For
these reasons, specifying a radius of zero is allowed but is not recommended.

@var rcConfig::maxEdgeLen
@par

In certain cases, long outer edges may decrease the quality of the resulting 
triangulation, creating very long thin triangles. This can sometimes be 
remedied by limiting the maximum edge length, causing the problematic long 
edges to be broken up into smaller segments. 

The parameter #maxEdgeLen defines the maximum edge length and is defined in 
terms of voxels. A good value for #maxEdgeLen is something like 
`walkableRadius * 8`. A good way to adjust this value is to first set it really 
high and see if your data creates long edges. If it does, decrease #maxEdgeLen
until you find the largest value which improves the resulting tesselation.

Extra vertices will be inserted as needed to keep contour edges below this
length. A value of zero effectively disables this feature.

@var rcConfig::maxSimplificationError
@par

When the rasterized areas are converted back to a vectorized representation, 
the #maxSimplificationError describes how loosely the simplification is done.
The simplification process uses the 
<a href="https://en.wikipedia.org/wiki/Ramer–Douglas–Peucker_algorithm">Ramer–Douglas-Peucker algorithm</a>,
and this value describes the max deviation in voxels.

Good values for #maxSimplificationError are in the range `[1.1, 1.5]`.  
A value of `1.3` is a good starting point and usually yields good results. 
If the value is less than `1.1`, some sawtoothing starts to appear at the 
generated edges.  If the value is more than `1.5`, the mesh simplification 
starts to cut some corners it shouldn't.

The effect of this parameter only applies to the xz-plane.

@var rcConfig::minRegionArea
@par

Watershed partitioning is really prone to noise in the input distance field. 
In order to get nicer areas, the areas are merged and small disconnected areas 
are removed after the water shed partitioning. The parameter #minRegionArea 
describes the minimum isolated region size that is still kept. A region is 
removed if the number of voxels in the region is less than the square of 
#minRegionArea.

Any regions that are smaller than this area will be marked as unwalkable.
This is useful in removing useless regions that can sometimes form on 
geometry such as table tops, box tops, etc.

@var rcConfig::maxVertsPerPoly
@par

If the mesh data is to be used to construct a Detour navigation mesh, then the upper limit
is limited to <= #DT_VERTS_PER_POLYGON.

@var rcConfig::mergeRegionArea
@par

The triangulation process works best with small, localized voxel regions. 
The parameter #mergeRegionArea controls the maximum voxel area of a region 
that is allowed to be merged with another region.  If you see small patches 
missing here and there, you could lower the #minRegionArea value.

@struct rcHeightfield
@par

The grid of a heightfield is layed out on the xz-plane based on the
value of #cs.  Spans exist within the grid columns with the span
min/max values at increments of #ch from the base of the grid.  The smallest 
possible span size is <tt>(#cs width) * (#cs depth) * (#ch height)</tt>. (Which is a single voxel.)

The standard process for buidling a heightfield is to allocate it using
#rcAllocHeightfield, initialize it using #rcCreateHeightfield, then
add spans using the various helper functions such as #rcRasterizeTriangle.

Building a heightfield is one of the first steps in creating a polygon mesh
from source geometry.  After it is populated, it is used to build a 
rcCompactHeightfield.

Example of iterating the spans in a heightfield:
@code
// Where hf is a reference to an heightfield object.

const float* orig = hf.bmin;
const float cs = hf.cs;
const float ch = hf.ch;

const int w = hf.width;
const int h = hf.height;

for (int y = 0; y < h; ++y)
{
    for (int x = 0; x < w; ++x)
    {
        // Deriving the minimum corner of the grid location.
        float fx = orig[0] + x*cs;
        float fz = orig[2] + y*cs;
        // The base span in the column. (May be null.)
        const rcSpan* s = hf.spans[x + y*w]; 
        while (s)
        {
            // Detriving the minium and maximum world position of the span.
            float fymin = orig[1]+s->smin*ch;
            float fymax = orig[1] + s->smax*ch;
            // Do other things with the span before moving up the column.
            s = s->next;
        }
    }
}
@endcode

@see rcAllocHeightfield, rcFreeHeightField, rcCreateHeightfield

@struct rcCompactCell
@par

See the rcCompactHeightfield documentation for an example of how compact cells
are used to iterate the heightfield.

Useful instances of this type can only by obtained from a #rcCompactHeightfield object.

@see rcCompactHeightfield

@struct rcCompactSpan
@par

The span represents open, unobstructed space within a compact heightfield column.
See the rcCompactHeightfield documentation for an example of iterating spans and searching 
span connections.

Useful instances of this type can only by obtained from a #rcCompactHeightfield object.

@see rcCompactHeightfield


@struct rcCompactHeightfield
@par

For this type of heightfield, the spans represent the open (unobstructed) 
space above the solid surfaces of a voxel field. It is usually created from 
a #rcHeightfield object.  Data is stored in a compact, efficient manner,  
but the structure is not condusive to adding and removing spans.

The standard process for buidling a compact heightfield is to allocate it 
using #rcAllocCompactHeightfield, build it using #rcBuildCompactHeightfield,
then run it through the various helper functions to generate neighbor
and region data.

Connected neighbor spans form non-overlapping surfaces.  When neighbor 
information is generated, spans will include data that can be used to 
locate axis-neighbors. Axis-neighbors are connected
spans that are offset from the current cell column as follows:
<pre>
Direction 0 = (-1, 0)
Direction 1 = (0, 1)
Direction 2 = (1, 0)
Direction 3 = (0, -1)
</pre>

Example of iterating and inspecting spans, including connected neighbors:

@code
// Where chf is an instance of a rcCompactHeightfield.

const float cs = chf.cs;
const float ch = chf.ch;

for (int y = 0; y < chf.height; ++y)
{
    for (int x = 0; x < chf.width; ++x)
    {
        // Deriving the minimum corner of the grid location.
        const float fx = chf.bmin[0] + x*cs;
        const float fz = chf.bmin[2] + y*cs;

        // Get the cell for the grid location then iterate
        // up the column.
        const rcCompactCell& c = chf.cells[x+y*chf.width];
        for (unsigned i = c.index, ni = c.index+c.count; i < ni; ++i)
        {
            const rcCompactSpan& s = chf.spans[i];

            Deriving the minimum (floor) of the span.
            const float fy = chf.bmin[1] + (s.y+1)*ch;

            // Testing the area assignment of the span.
            if (chf.areas[i] == RC_WALKABLE_AREA)
            { 
                // The span is in the default 'walkable area'.
            }
            else if (chf.areas[i] == RC_NULL_AREA)
            { 
                // The surface is not considered walkable.
                // E.g. It was filtered out during the build processes.
            }
            else
            { 
                // Do something. (Only applicable for custom build
                // build processes.)
            }

            // Iterating the connected axis-neighbor spans.
            for (int dir = 0; dir < 4; ++dir)
            {
                if (rcGetCon(s, dir) != RC_NOT_CONNECTED)
                {
                    // There is a neighbor in this direction.
                    const int nx = x + rcGetDirOffsetX(dir);
                    const int ny = y + rcGetDirOffsetY(dir);
                    const int ni = (int)chf.cells[nx+ny*w].index + rcGetCon(s, 0);
                    const rcCompactSpan& ns = chf.spans[ni];
                    // Do something with the neighbor span.
                }
            }
        }
    }
}
@endcode

@see rcAllocCompactHeightfield, rcFreeCompactHeightfield, rcBuildCompactHeightfield

@struct rcContour
@par

A contour only exists within the context of a #rcContourSet object.

While the height of the contour's border may vary, the contour will always 
form a simple polygon when projected onto the xz-plane.

Example of converting vertices into world space:

@code
// Where cset is the rcContourSet object to which the contour belongs.
float worldX = cset.bmin[0] + vertX * cset.cs;
float worldY = cset.bmin[1] + vertY * cset.ch;
float worldZ = cset.bmin[2] + vertZ * cset.cs;
@endcode

@see rcContourSet

@var rcContour::verts
@par

The simplified contour is a version of the raw contour with all 
'unnecessary' vertices removed. Whether a vertex is 
considered unnecessary depends on the contour build process.

The data format is as follows: (x, y, z, r) * #nverts

A contour edge is formed by the current and next vertex. The r-value 
represents region and connection information for the edge. For example:

@code
int r = verts[i*4+3];

int regionId = r & RC_CONTOUR_REG_MASK;

if (r & RC_BORDER_VERTEX)
{
    // The edge represents a solid border.
}

if (r & RC_AREA_BORDER)
{
    // The edge represents a transition between different areas.
}
@endcode

@var rcContour::rverts
@par

See #verts for information on element layout.

@struct rcContourSet
@par

All contours within the set share the minimum bounds and cell sizes of the set.

The standard process for building a contour set is to allocate it
using #rcAllocContourSet, then initialize it using #rcBuildContours.

@see rcAllocContourSet, rcFreeContourSet, rcBuildContours

@struct rcPolyMesh
@par

A mesh of potentially overlapping convex polygons of between three 
and #nvp vertices. The mesh exists within the context of an axis-aligned 
bounding box (AABB) with vertices laid out in an evenly spaced grid, based 
on the values of #cs and #ch.

The standard process for building a contour set is to allocate it using
#rcAllocPolyMesh, the initialize it using #rcBuildPolyMesh

Example of iterating the polygons:

@code
// Where mesh is a reference to a rcPolyMesh object.

const int nvp = mesh.nvp;
const float cs = mesh.cs;
const float ch = mesh.ch;
const float* orig = mesh.bmin;

for (int i = 0; i < mesh.npolys; ++i)
{
   const unsigned short* p = &mesh.polys[i*nvp*2];
   
    // Iterate the vertices.
   unsigned short vi[3];  // The vertex indices.
   for (int j = 0; j < nvp; ++j)
   {
      if (p[j] == RC_MESH_NULL_IDX) 
            break; // End of vertices.

        if (p[j + nvp] == RC_MESH_NULL_IDX)
        {
            // The edge beginning with this vertex is a solid border.
        }
        else
        {
            // The edge beginning with this vertex connects to 
            // polygon p[j + nvp].
        }
        
        // Convert to world space.
       const unsigned short* v = &mesh.verts[p[j]*3];
      const float x = orig[0] + v[0]*cs;
      const float y = orig[1] + v[1]*ch;
      const float z = orig[2] + v[2]*cs;
      // Do something with the vertices.
   }
}
@endcode

@see rcAllocPolyMesh, rcFreePolyMesh, rcBuildPolyMesh

@var rcPolyMesh::verts
@par

The values of #bmin ,#cs, and #ch are used to convert vertex coordinates
to world space as follows:

@code
float worldX = bmin[0] + verts[i*3+0] * cs
float worldY = bmin[1] + verts[i*3+1] * ch
float worldZ = bmin[2] + verts[i*3+2] * cs
@endcode

@var rcPolyMesh::polys
@par

Each entry is <tt>2 * #nvp</tt> in length. The first half of the entry 
contains the indices of the polygon. The first instance of #RC_MESH_NULL_IDX
indicates the end of the indices for the entry. The second half contains 
indices to neighbor polygons. A value of #RC_MESH_NULL_IDX indicates no 
connection for the associated edge. (I.e. The edge is a solid border.)

For example:
<pre>
nvp = 6
For the entry: (1, 3, 4, 8, RC_MESH_NULL_IDX, RC_MESH_NULL_IDX, 
                18, RC_MESH_NULL_IDX , 21, RC_MESH_NULL_IDX, RC_MESH_NULL_IDX, RC_MESH_NULL_IDX)

(1, 3, 4, 8) defines a polygon with 4 vertices.
Edge 1->3 is shared with polygon 18.
Edge 4->8 is shared with polygon 21.
Edges 3->4 and 4->8 are border edges not shared with any other polygon.
</pre>

@var rcPolyMesh::areas
@par

The standard build process assigns the value of #RC_WALKABLE_AREA to all walkable polygons.
This value can then be changed to meet user requirements.

@struct rcPolyMeshDetail
@par

The detail mesh is made up of triangle sub-meshes that provide extra 
height detail for each polygon in its assoicated polygon mesh.

The standard process for building a detail mesh is to allocate it 
using #rcAllocPolyMeshDetail, then build it using #rcBuildPolyMeshDetail.

See the individual field definitions for details realted to the structure
the mesh.

@see rcAllocPolyMeshDetail, rcFreePolyMeshDetail, rcBuildPolyMeshDetail, rcPolyMesh

@var rcPolyMeshDetail::meshes
@par

[(baseVertIndex, vertCount, baseTriIndex, triCount) * #nmeshes]

Maximum number of vertices per sub-mesh: 127<br/>
Maximum number of triangles per sub-mesh: 255

The sub-meshes are stored in the same order as the polygons from the
rcPolyMesh they represent.  E.g. rcPolyMeshDetail sub-mesh 5 is associated
with #rcPolyMesh polygon 5.

Example of iterating the triangles in a sub-mesh.

@code
// Where dmesh is a reference to a rcPolyMeshDetail object.

// Iterate the sub-meshes. (One for each source polygon.)
for (int i = 0; i < dmesh.nmeshes; ++i)
{
	const unsigned int* meshDef = &dmesh.meshes[i*4];
	const unsigned int baseVerts = meshDef[0];
	const unsigned int baseTri = meshDef[2];
	const int ntris = (int)meshDef[3];	
	
	const float* verts = &dmesh.verts[baseVerts*3];
	const unsigned char* tris = &dmesh.tris[baseTri*4];

    // Iterate the sub-mesh's triangles.
	for (int j = 0; j < ntris; ++j)
	{
		const float x = verts[tris[j*4+0]*3];
		const float y = verts[tris[j*4+1]*3];
		const float z = verts[tris[j*4+2]*3];
		// Do something with the vertex.
	}
}
@endcode

@var rcPolyMeshDetail::verts
@par

[(x, y, z) * #nverts] 

The vertices are grouped by sub-mesh and will contain duplicates since 
each sub-mesh is independently defined.

The first group of vertices for each sub-mesh are in the same order as 
the vertices for the sub-mesh's associated PolyMesh polygon. These 
vertices are followed by any additional detail vertices. So it the 
associated polygon has 5 vertices, the sub-mesh will have a minimum 
of 5 vertices and the first 5 vertices will be equivalent to the 5 
polygon vertices.

@var rcPolyMeshDetail::tris
@par

[(vertIndexA, vertIndexB, vertIndexC, flags) * #ntris] 

The triangles are grouped by sub-mesh.

<b>Vertex Indices</b>

The vertex indices in the triangle array are local to the sub-mesh, not global. 
To translate into an global index in the vertices array, the values must be 
offset by the sub-mesh's base vertex index.

Example: If the baseVertexIndex for the sub-mesh is 5 and the triangle entry 
is (4, 8, 7, 0), then the actual indices for the vertices are (4 + 5, 8 + 5, 7 + 5).

@b Flags

The flags entry indicates which edges are internal and which are external to 
the sub-mesh. Internal edges connect to other triangles within the same sub-mesh. 
External edges represent portals to other sub-meshes or the null region.

Each flag is stored in a 2-bit position. Where position 0 is the lowest 2-bits 
and position 4 is the highest 2-bits:

<tt>
Position 0: Edge AB (>> 0)<br/>
Position 1: Edge BC (>> 2)<br/>
Position 2: Edge CA (>> 4)<br/>
Position 4: Unused<br/>
</tt>

Testing can be performed as follows:

@code
if (((flags >> 2) & 0x3) != 0)
{
    // Edge BC is an external edge.
}
@endcode

@fn void rcSetCon(rcCompactSpan &s, int dir, int i)
@par

This function is used by the build process. It is rarely of use to end users.

@see #rcCompactHeightfield, #rcCompactSpan

@fn int rcGetCon(const rcCompactSpan &s, int dir)
@par

Can be used to locate neighbor spans in a compact heightfield. See the 
#rcCompactHeightfield documentation for details on its use.

@see #rcCompactHeightfield, #rcCompactSpan

@fn int rcGetDirOffsetX(int dir)
@par

The value of @p dir will be automatically wrapped. So a value of 6 will be interpreted as 2.

See the #rcCompactHeightfield documentation for usage details.

@fn int rcGetDirOffsetY(int dir)
@par

The value of @p dir will be automatically wrapped. So a value of 6 will be interpreted as 2.

See the #rcCompactHeightfield documentation for usage details.

*/
