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Recast: major improvements to traverse link algorithm

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From now on, internal links are connected first before external neighbor links. This now also happens in the same pass which improves performance (this yields better results and behavior after the last few and current changes).

Also added a fine tunable test dictating whether links should only connect when edges overlap, or when one of the edges overlap (can be tweaked by setting an elevation trigger, by skipping out on lower elevations if this deems necessary, but typically doesn't).

The slope angle option was originally in the table but removed. After reconsideration this has been brought back in as you cannot define min/max slopes with 3d distances and elevation differences. The distance either needs to be 2d (which will break the max 2550.f distance per link rule), or an additional slope check has to be used to define this properly.

 After a lot of fine tuning, the results appear to be almost identical to the original navmeshes shipped with Respawn games. The algorithm is also a lot faster now (went from 30 seconds to 8 seconds on the staging area with much better and more accurate results).
This commit is contained in:
Kawe Mazidjatari 2024-08-28 14:06:11 +02:00
parent f9fb1c6c64
commit b144b200ad
3 changed files with 189 additions and 90 deletions
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268
src/naveditor/Editor.cpp
View File

@ -72,55 +72,51 @@ TraverseType_s s_traverseTable[NUM_TRAVERSE_TYPES];
static void initTraverseTableParams()
{
s_traverseTable[0] = { 0.0f, 0.0f, 0, 0 }; // Unused
s_traverseTable[0] = { 0.f, 0.f, 0.f, 0.f, 0.f, 0.f, -1.f, false }; // Unused
s_traverseTable[1] = { 0, 48, 10, 120 }; //1
s_traverseTable[2] = { 48, 96, 120, 160 }; //2
s_traverseTable[3] = { 96, 128, 160, 220 }; //3
s_traverseTable[1] = { 10.f, 120.f, 0.f, 48.f, 0.f, 67.f, -1.f, false };
s_traverseTable[2] = { 120.f, 160.f, 48.f, 96.f, 5.f, 78.f, 0.f, false };
s_traverseTable[3] = { 160.f, 220.f, 0.f, 128.f, 0.f, 38.f, 0.f, false };
s_traverseTable[4] = { 0.0f, 0.0f, 0, 0 }; // Unused
s_traverseTable[5] = { 0.0f, 0.0f, 0, 0 }; // Unused
s_traverseTable[6] = { 0.0f, 0.0f, 0, 0 }; // Unused
s_traverseTable[4] = { 0.f, 0.f, 0.f, 0.f, 0.f, 0.f, -1.f, false }; // Unused
s_traverseTable[5] = { 0.f, 0.f, 0.f, 0.f, 0.f, 0.f, -1.f, false }; // Unused
s_traverseTable[6] = { 0.f, 0.f, 0.f, 0.f, 0.f, 0.f, -1.f, false }; // Unused
s_traverseTable[7] = { 0, 96, 800, 1030 }; //7
s_traverseTable[8] = { 64, 168, 70, 210 }; //8
s_traverseTable[9] = { 168, 384, 210, 450 }; //9
s_traverseTable[10] = { 384, 672, 450, 860 }; //10
s_traverseTable[11] = { 0, 56, 410, 940 }; //11
s_traverseTable[12] = { 348, 640, 640, 930 }; //12
s_traverseTable[13] = { 256, 640, 810, 1220 }; //13
s_traverseTable[7] = { 800.f, 1030.f, 0.f, 96.f, 0.0f, 6.5f, -1.f, false };
s_traverseTable[8] = { 70.f, 220.f, 48.f, 220.f, 19.f, 84.f, 0.f, false };
s_traverseTable[9] = { 210.f, 450.f, 168.f, 384.f, 27.f, 87.5f, 0.f, false };
s_traverseTable[10] = { 450.f, 860.f, 384.f, 672.f, 44.f, 89.5f, 0.f, false };
s_traverseTable[11] = { 410.f, 940.f, 0.f, 56.f, 0.f , 7.f, 0.f, true };
s_traverseTable[12] = { 640.f, 930.f, 348.f, 640.f, 2.2f, 47.f, 0.f, true };
s_traverseTable[13] = { 810.f, 1220.f, 256.f, 640.f, 5.7f, 58.5f, 0.f, true };
s_traverseTable[14] = { 0.0f, 0.0f, 0, 0 }; // Unused
s_traverseTable[15] = { 0.0f, 0.0f, 0, 0 }; // Off-mesh links?
s_traverseTable[14] = { 0.f, 0.f, 0.f, 0.f, 0.f, 0.f, -1, false }; // Unused
s_traverseTable[15] = { 0.f, 0.f, 0.f, 0.f, 0.f, 0.f, -1, false }; // Off-mesh links only, see 'level_script.ent'
s_traverseTable[16] = { 0, 104, 220, 410 };
s_traverseTable[17] = { 104, 416, 410, 640 };
s_traverseTable[16] = { 220.f, 410.f, 0.f, 104.f, 0.f, 12.5f, 0.f, false };
s_traverseTable[17] = { 410.f, 640.f, 104.f, 416.f, 4.6f, 53.f, 0.f, true };
s_traverseTable[18] = { 0.0f, 0.0f, 0, 0 }; // Off-mesh links?
s_traverseTable[18] = { 0.0f, 0.0f, 0.f, 0.f, 0.f, 0.f, -1.f, false }; // Off-mesh links only, see 'level_script.ent'
#if DT_NAVMESH_SET_VERSION > 5
s_traverseTable[19] = { 0.0f, 0.0f, 0, 0 }; // Unused
s_traverseTable[20] = { 120, 330, 160, 400 }; // Maps to type 19 in MSET 5
s_traverseTable[21] = { 104, 416, 330, 640 }; // Maps to type 20 in MSET 5
s_traverseTable[19] = { 0.f, 0.f, 0.f, 0.f, 0.f, 0.f, -1.f, false }; // Unused
s_traverseTable[20] = { 256.f, 400.f, 256.f, 330.f, 34.f, 89.f, 0.f, false }; // Maps to type 19 in MSET 5
s_traverseTable[21] = { 0.f, 1250.f, 340.f, 1250.f, 46.f, 89.f, 0.f, false }; // Maps to type 20 in MSET 5
#else
s_traverseTable[19] = { 120, 330, 160, 400 }; // Maps to type 19 in MSET 5
s_traverseTable[20] = { 104, 416, 330, 640 }; // Maps to type 20 in MSET 5
s_traverseTable[21] = { 0.0f, 0.0f, 0, 0 }; // Unused
s_traverseTable[19] = { 256.f, 400.f, 256.f, 330.f, 34.f, 89.f, 0.f, false }; // Maps to type 19 in MSET 5
s_traverseTable[20] = { 0.f, 1250.f, 340.f, 1250.f, 46.f, 89.f, 0.f, false }; // Maps to type 20 in MSET 5
s_traverseTable[21] = { 0.f, 0.f, 0.f, 0.f, 0.f, 0.f, -1.f, false }; // Unused
#endif
s_traverseTable[22] = { 0.0f, 0.0f, 0, 0 }; // Unused
s_traverseTable[23] = { 0.0f, 0.0f, 0, 0 }; // Unused
s_traverseTable[24] = { 0, 0, 0, 0 }; // Does not exist in MSET 5 ~ 8.
s_traverseTable[25] = { 0.0f, 0.0f, 0, 0 }; // Unused
s_traverseTable[26] = { 0.0f, 0.0f, 0, 0 }; // Unused
s_traverseTable[27] = { 0.0f, 0.0f, 0, 0 }; // Unused
s_traverseTable[28] = { 0.0f, 0.0f, 0, 0 }; // Unused
s_traverseTable[29] = { 0.0f, 0.0f, 0, 0 }; // Unused
s_traverseTable[30] = { 0.0f, 0.0f, 0, 0 }; // Unused
s_traverseTable[31] = { 0.0f, 0.0f, 0, 0 }; // Unused
s_traverseTable[22] = { 0.f, 0.f, 0.f, 0.f, 0.f, 0.f, -1.f, false }; // Unused
s_traverseTable[23] = { 0.f, 0.f, 0.f, 0.f, 0.f, 0.f, -1.f, false }; // Unused
s_traverseTable[24] = { 0.f, 0.f, 0.f, 0.f, 0.f, 0.f, -1.f, false }; // Does not exist in MSET 5 ~ 8.
s_traverseTable[25] = { 0.f, 0.f, 0.f, 0.f, 0.f, 0.f, -1.f, false }; // Unused
s_traverseTable[26] = { 0.f, 0.f, 0.f, 0.f, 0.f, 0.f, -1.f, false }; // Unused
s_traverseTable[27] = { 0.f, 0.f, 0.f, 0.f, 0.f, 0.f, -1.f, false }; // Unused
s_traverseTable[28] = { 0.f, 0.f, 0.f, 0.f, 0.f, 0.f, -1.f, false }; // Unused
s_traverseTable[29] = { 0.f, 0.f, 0.f, 0.f, 0.f, 0.f, -1.f, false }; // Unused
s_traverseTable[30] = { 0.f, 0.f, 0.f, 0.f, 0.f, 0.f, -1.f, false }; // Unused
s_traverseTable[31] = { 0.f, 0.f, 0.f, 0.f, 0.f, 0.f, -1.f, false }; // Unused
}
Editor::Editor() :
@ -259,6 +255,7 @@ void Editor::resetCommonSettings()
m_cellSize = 16.0f;
m_cellHeight = 5.85f;
m_traverseLinkDrawParams.dynamicOffset = m_traverseRayDynamicOffset;
m_traverseLinkDrawParams.cellHeight = m_cellHeight;
// todo(amos): check if this applies for all hulls, and check if this is the
@ -270,7 +267,8 @@ void Editor::resetCommonSettings()
// https://developer.valvesoftware.com/wiki/Pl/Dimensions
m_agentMaxSlope = 45.573f;
m_traverseRayExtraOffset = 0.0f;
m_traverseRayExtraOffset = 8.0f;
m_traverseEdgeMinOverlap = RD_EPS;
m_regionMinSize = 8;
m_regionMergeSize = 20;
@ -431,17 +429,17 @@ void Editor::handleCommonSettings()
static int frozenCols = 1;
static int frozenRows = 2;
const int rowsCount = NUM_TRAVERSE_TYPES;
const float textBaseHeight = ImGui::GetTextLineHeightWithSpacing();
const char* columnNames[] = { "Type", "minElev", "maxElev", "minDist", "maxDist" };
const int columnsCount = IM_ARRAYSIZE(columnNames);
const int rowsCount = NUM_TRAVERSE_TYPES;
const char* linearColumnNames[] = { "Type", "minDist", "maxDist", "minElev", "maxElev"};
const int linearColumnsCount = IM_ARRAYSIZE(linearColumnNames);
if (ImGui::BeginTable("TraverseTableFineTuner", columnsCount, tableFlags, ImVec2(0.0f, (textBaseHeight * 12)+10.f)))
if (ImGui::BeginTable("TraverseTableLinearFineTuner", linearColumnsCount, tableFlags, ImVec2(0.0f, (textBaseHeight * 12)+10.f)))
{
ImGui::TableSetupColumn(columnNames[0], ImGuiTableColumnFlags_NoHide | ImGuiTableColumnFlags_NoReorder);
for (int n = 1; n < columnsCount; n++)
ImGui::TableSetupColumn(columnNames[n], columnFlags, 100);
ImGui::TableSetupColumn(linearColumnNames[0], ImGuiTableColumnFlags_NoHide | ImGuiTableColumnFlags_NoReorder);
for (int n = 1; n < linearColumnsCount; n++)
ImGui::TableSetupColumn(linearColumnNames[n], columnFlags, 100);
ImGui::TableSetupScrollFreeze(frozenCols, frozenRows);
ImGui::TableAngledHeadersRow();
@ -460,7 +458,7 @@ void Editor::handleCommonSettings()
ImGui::AlignTextToFramePadding();
ImGui::Text("%d", row);
for (int column = 1; column < columnsCount; column++)
for (int column = 1; column < linearColumnsCount; column++)
{
if (!ImGui::TableSetColumnIndex(column))
continue;
@ -472,18 +470,16 @@ void Editor::handleCommonSettings()
switch (column)
{
case 1:
trav.minElev = rdClamp(trav.minElev, 0.0f, trav.maxElev);
ImGui::SliderFloat("", &trav.minElev, 0, trav.maxElev);
ImGui::SliderFloat("", &trav.minDist, 0, trav.maxDist, "%g");
break;
case 2:
ImGui::SliderFloat("", &trav.maxElev, 0, DT_TRAVERSE_DIST_MAX);
ImGui::SliderFloat("", &trav.maxDist, 0, DT_TRAVERSE_DIST_MAX, "%g");
break;
case 3:
trav.minDist = rdClamp(trav.minDist, 0.0f, trav.maxDist);
ImGui::SliderFloat("", &trav.minDist, 0, trav.maxDist);
ImGui::SliderFloat("", &trav.minElev, 0, trav.maxElev, "%g");
break;
case 4:
ImGui::SliderFloat("", &trav.maxDist, 0, DT_TRAVERSE_DIST_MAX);
ImGui::SliderFloat("", &trav.maxElev, 0, DT_TRAVERSE_DIST_MAX, "%g");
break;
}
@ -496,6 +492,68 @@ void Editor::handleCommonSettings()
ImGui::EndTable();
}
const char* angularColumnNames[] = { "Type", "minSlope", "maxSlope", "ovlpTrig", "ovlpExcl" };
const int angularColumnsCount = IM_ARRAYSIZE(angularColumnNames);
if (ImGui::BeginTable("TraverseTableAngularFineTuner", angularColumnsCount, tableFlags, ImVec2(0.0f, (textBaseHeight * 12) + 10.f)))
{
ImGui::TableSetupColumn(angularColumnNames[0], ImGuiTableColumnFlags_NoHide | ImGuiTableColumnFlags_NoReorder);
for (int n = 1; n < angularColumnsCount; n++)
ImGui::TableSetupColumn(angularColumnNames[n], columnFlags, 100);
ImGui::TableSetupScrollFreeze(frozenCols, frozenRows);
ImGui::TableAngledHeadersRow();
ImGui::TableHeadersRow();
ImGuiListClipper clipper;
clipper.Begin(rowsCount);
while (clipper.Step())
{
for (int row = clipper.DisplayStart; row < clipper.DisplayEnd; row++)
{
ImGui::PushID(row);
ImGui::TableNextRow();
ImGui::TableSetColumnIndex(0);
ImGui::AlignTextToFramePadding();
ImGui::Text("%d", row);
for (int column = 1; column < angularColumnsCount; column++)
{
if (!ImGui::TableSetColumnIndex(column))
continue;
ImGui::PushID(column);
ImGui::PushItemWidth(-FLT_MIN); // Right align cells.
TraverseType_s& trav = s_traverseTable[row];
switch (column)
{
case 1:
ImGui::SliderFloat("", &trav.minSlope, 0, trav.maxSlope, "%g");
break;
case 2:
ImGui::SliderFloat("", &trav.maxSlope, 0, 360, "%g");
break;
case 3:
ImGui::SliderFloat("", &trav.ovlpTrig, 0, trav.maxElev, "%g");
break;
case 4:
ImGui::Checkbox("", &trav.ovlpExcl);
break;
}
ImGui::PopItemWidth();
ImGui::PopID();
}
ImGui::PopID();
}
}
ImGui::EndTable();
}
if (ImGui::Button("Reset Traverse Table Parameters"))
initTraverseTableParams();
@ -564,6 +622,7 @@ void Editor::handleCommonSettings()
if (ImGui::SliderFloat("Extra Offset", &m_traverseRayExtraOffset, 0, 128))
m_traverseLinkDrawParams.extraOffset = m_traverseRayExtraOffset;
ImGui::SliderFloat("Min Overlap", &m_traverseEdgeMinOverlap, 0.0f, m_tileSize*m_cellSize, "%g");
ImGui::Separator();
}
@ -597,7 +656,7 @@ void Editor::handleUpdate(const float dt)
updateToolStates(dt);
}
TraverseType_e GetBestTraverseType(const float elevation, const float traverseDist)
TraverseType_e GetBestTraverseType(const float traverseDist, const float elevation, const float slope, const bool baseOverlaps, const bool landOverlaps)
{
TraverseType_e bestTraverseType = INVALID_TRAVERSE_TYPE;
float smallestDiff = FLT_MAX;
@ -607,14 +666,8 @@ TraverseType_e GetBestTraverseType(const float elevation, const float traverseDi
const TraverseType_s& traverseType = s_traverseTable[i];
// Skip unused types...
if (traverseType.minElev == 0.0f && traverseType.maxElev == 0.0f &&
traverseType.minDist == 0 && traverseType.maxDist == 0)
{
continue;
}
if (elevation < traverseType.minElev ||
elevation > traverseType.maxElev)
if (traverseType.minDist == 0.0f && traverseType.maxDist == 0.0f &&
traverseType.minElev == 0.0f && traverseType.maxElev == 0.0f)
{
continue;
}
@ -625,12 +678,37 @@ TraverseType_e GetBestTraverseType(const float elevation, const float traverseDi
continue;
}
const float midElev = (traverseType.minElev+traverseType.maxElev) / 2.0f;
const float midDist = (traverseType.minDist+traverseType.maxDist) / 2.0f;
const float elevDiff = rdMathFabsf(elevation-midElev);
const float distDiff = rdMathFabsf(traverseDist-midDist);
if (elevation < traverseType.minElev ||
elevation > traverseType.maxElev)
{
continue;
}
const float totalDiff = elevDiff+distDiff;
if (slope < traverseType.minSlope ||
slope > traverseType.maxSlope)
{
continue;
}
if (traverseType.ovlpTrig > -1 && elevation >= traverseType.ovlpTrig)
{
const bool noOverlap = traverseType.ovlpExcl
? (!baseOverlaps && !landOverlaps)
: (!baseOverlaps || !landOverlaps);
if (noOverlap)
continue;
}
const float midDist = (traverseType.minDist+traverseType.maxDist) / 2.0f;
const float midElev = (traverseType.minElev+traverseType.maxElev) / 2.0f;
const float midSlope = (traverseType.minSlope+traverseType.maxSlope) / 2.0f;
const float distDiff = rdMathFabsf(traverseDist-midDist);
const float elevDiff = rdMathFabsf(elevation-midElev);
const float slopeDiff = rdMathFabsf(slope-midSlope);
const float totalDiff = elevDiff+distDiff+slopeDiff;
if (totalDiff < smallestDiff)
{
@ -642,6 +720,26 @@ TraverseType_e GetBestTraverseType(const float elevation, const float traverseDi
return bestTraverseType;
}
float calcEdgeOverlap(const float* edge1Start, const float* edge1End, const float* edge2Start, const float* edge2End, const float* targetEdgeVec)
{
float min1 = rdVproj2D(edge1Start, targetEdgeVec);
float max1 = rdVproj2D(edge1End, targetEdgeVec);
if (min1 > max1)
rdSwap(min1, max1);
float min2 = rdVproj2D(edge2Start, targetEdgeVec);
float max2 = rdVproj2D(edge2End, targetEdgeVec);
if (min2 > max2)
rdSwap(min2, max2);
const float start = rdMax(min1, min2);
const float end = rdMin(max1, max2);
return rdMax(0.0f, end - start);
}
static bool polyEdgeFaceAgainst(const float* v1, const float* v2, const float* n1, const float* n2)
{
const float delta[2] = { v2[0] - v1[0], v2[1] - v1[1] };
@ -807,14 +905,14 @@ void Editor::connectTileTraverseLinks(dtMeshTile* const baseTile, const bool lin
const float* const basePolySpos = &baseTile->verts[basePoly->verts[j] * 3];
const float* const basePolyEpos = &baseTile->verts[basePoly->verts[(j + 1) % basePoly->vertCount] * 3];
float basePolyEdgeMid[3];
rdVsad(basePolyEdgeMid, basePolySpos, basePolyEpos, 0.5f);
float baseEdgeDir[3];
rdVsub(baseEdgeDir, basePolyEpos, basePolySpos);
unsigned char baseSide = rdClassifyPointInsideBounds(basePolyEdgeMid, baseHeader->bmin, baseHeader->bmax);
unsigned char baseSide = rdClassifyDirection(baseEdgeDir, baseHeader->bmin, baseHeader->bmax);
const int MAX_NEIS = 32; // Max neighbors
dtMeshTile* neis[MAX_NEIS];
int nneis = 0;
if (linkToNeighbor) // Retrieve the neighboring tiles on the side of our base poly edge.
@ -832,6 +930,10 @@ void Editor::connectTileTraverseLinks(dtMeshTile* const baseTile, const bool lin
neis[0] = baseTile;
}
float basePolyEdgeMid[3];
if (nneis)
rdVsad(basePolyEdgeMid, basePolySpos, basePolyEpos, 0.5f);
for (int k = nneis-1; k >= 0; --k)
{
dtMeshTile* landTile = neis[k];
@ -894,8 +996,7 @@ void Editor::connectTileTraverseLinks(dtMeshTile* const baseTile, const bool lin
if (quantDist == 0)
continue; // Link distance is greater than maximum supported.
float baseEdgeDir[3], landEdgeDir[3];
rdVsub(baseEdgeDir, basePolyEpos, basePolySpos);
float landEdgeDir[3];
rdVsub(landEdgeDir, landPolyEpos, landPolySpos);
const float dotProduct = rdVdot(baseEdgeDir, landEdgeDir);
@ -915,7 +1016,11 @@ void Editor::connectTileTraverseLinks(dtMeshTile* const baseTile, const bool lin
continue;
const float elevation = rdMathFabsf(basePolyEdgeMid[2]-landPolyEdgeMid[2]);
const TraverseType_e traverseType = GetBestTraverseType(elevation, dist);
const float slopeAngle = rdMathFabsf(rdCalcSlopeAngle(basePolyEdgeMid, landPolyEdgeMid));
const bool baseOverlaps = calcEdgeOverlap(basePolySpos, basePolyEpos, landPolySpos, landPolyEpos, baseEdgeDir) > m_traverseEdgeMinOverlap;
const bool landOverlaps = calcEdgeOverlap(landPolySpos, landPolyEpos, basePolySpos, basePolyEpos, landEdgeDir) > m_traverseEdgeMinOverlap;
const TraverseType_e traverseType = GetBestTraverseType(dist, elevation, slopeAngle, baseOverlaps, landOverlaps);
if (traverseType == DT_NULL_TRAVERSE_TYPE)
continue;
@ -973,7 +1078,6 @@ void Editor::connectTileTraverseLinks(dtMeshTile* const baseTile, const bool lin
if (m_traverseRayDynamicOffset)
{
const float totLedgeSpan = walkableRadius+m_traverseRayExtraOffset;
const float slopeAngle = rdMathFabsf(rdCalcSlopeAngle(basePolyEdgeMid, landPolyEdgeMid));
const float maxAngle = rdCalcMaxLOSAngle(totLedgeSpan, m_cellHeight);
offsetAmount = rdCalcLedgeSpanOffsetAmount(totLedgeSpan, slopeAngle, maxAngle);
@ -1041,17 +1145,6 @@ bool Editor::createTraverseLinks()
const int maxTiles = m_navMesh->getMaxTiles();
// First pass to connect edges between external tiles together.
for (int i = 0; i < maxTiles; i++)
{
dtMeshTile* baseTile = m_navMesh->getTile(i);
if (!baseTile || !baseTile->header)
continue;
connectTileTraverseLinks(baseTile, true);
}
// Second pass to use remaining links to connect internal edges on the same tile together.
for (int i = 0; i < maxTiles; i++)
{
dtMeshTile* baseTile = m_navMesh->getTile(i);
@ -1059,6 +1152,7 @@ bool Editor::createTraverseLinks()
continue;
connectTileTraverseLinks(baseTile, false);
connectTileTraverseLinks(baseTile, true);
}
return true;

2
src/naveditor/Editor_TileMesh.cpp
View File

@ -729,8 +729,8 @@ void Editor_TileMesh::buildTile(const float* pos)
dtMeshTile* tile = (dtMeshTile*)m_navMesh->getTileByRef(tileRef);
// Reconnect the traverse links.
connectTileTraverseLinks(tile, true);
connectTileTraverseLinks(tile, false);
connectTileTraverseLinks(tile, true);
dtTraverseTableCreateParams params;
createTraverseTableParams(&params);

9
src/naveditor/include/Editor.h
View File

@ -43,10 +43,14 @@ extern const hulldef hulls[5];
struct TraverseType_s
{
float minElev;
float maxElev;
float minDist;
float maxDist;
float minElev;
float maxElev;
float minSlope;
float maxSlope;
float ovlpTrig;
bool ovlpExcl;
};
enum TraverseType_e // todo(amos): move elsewhere
@ -278,6 +282,7 @@ protected:
float m_agentMaxClimb;
float m_agentMaxSlope;
float m_traverseRayExtraOffset;
float m_traverseEdgeMinOverlap;
int m_regionMinSize;
int m_regionMergeSize;
int m_edgeMaxLen;