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# Getting around non-connected vertex gaps in hardware tessellation displacement mapping

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### #1Husbjörn  Members   -  Reputation: 243

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Posted 26 June 2014 - 10:10 AM

Sorry for the long title, couldn't figure out how to express it shorter without being overly ambigious as to what this post is about.

Anyway, I've been poking around with displacement maping using the hardware tessellation features of DX11 for getting some more vertices to actually displace the last few days, for no particular reason other than to try it out so I'm not really looking for other ways to solve some specific problem.

Displacing a sphere or some other surface with completely connected faces work out as intended but issues obviously occur where there are multiple vertices with the same position but different normals (these vertices then get displaced in different directions and thus become disconnected => gaps appear in the geometry). I tried to mock up some simple solution to this by finding out which vertices share positions in my meshes and then setting a flag for these to tell my domain shader to not displace those vertices at all; it wouldn't be overly pretty but at least the mesh should be gapless and it hopefully wouldn't be too noticeable I reasoned. Of course this didn't work out very well (the whole subdivision patches generated from such overlapping vertices had their displacement factors set to 0 creating quite obvious, large frames around right angles and such). What I'm wondering is basically if this is a reasonable approach to try to refine further or if there are other ways to go about it that may be better? The only article on the topic I've managed to find mostly went on about the exquisitness of Bezier curves but didn't really seem to come to any conclusions (although maybe those would've been obvious to anyone having the required math skills).

Thankful for any pointers on this, the more I try to force this, the more it feels like I'm probably missing something.

As for my implementation of the tessellation, I've mostly based it around what is described in chapter 18.7 and 18.8 of Introduction to 3D Game Programming With DirectX 11 (http://www.amazon.com/Introduction-3D-Game-Programming-DirectX/dp/1936420228).

### #2MJP  Moderators   -  Reputation: 11038

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Posted 26 June 2014 - 06:33 PM

It's a common problem, and it's pretty hard to work around. You should read through this presentation for some ideas.

### #3Husbjörn  Members   -  Reputation: 243

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Posted 27 June 2014 - 03:34 AM

Thanks MJP.

I don't suppose there's any video / audio recording of the presentation using those slides available somewhere, possibly for a nominal fee?

On a more off-topic note, I recognize that avatar of yours but have been unable to remember the name of the show (or was it possibly a book?) it featured in, care to enlighten me?

### #4belfegor  Crossbones+   -  Reputation: 2575

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Posted 27 June 2014 - 04:41 AM

There is more details here , i am researching on solution to this problem also.

### #5belfegor  Crossbones+   -  Reputation: 2575

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Posted 27 June 2014 - 07:24 AM

I think i have implemented index buffer for PN-AEN as described in that pdf document, but once i finished i saw that patch funcion HS_Constant is missing from shader that they have provided in appendix.

Copy-paste error.

D3D11 ERROR: ID3D11DeviceContext::DrawIndexed: Mismatched topology. Current Hull Shader expects input Control Point count of 3, but Input Assembler topology defines a patch list with 9 Control Points per patch. [ EXECUTION ERROR #2097222: DEVICE_DRAW_HULL_SHADER_INPUT_TOPOLOGY_MISMATCH]

Damn. Why did they provide code that does not work.

edit 6841:

I get shader to work this time but i am not sure if i have indices right as i see no displacement.

if i add displacement along normal:

... // domain shader
float3 n = mul(f3Normal, (float3x3)g_f4x4WorldView);
n = normalize(n);
f3EyePosition += n * 0.02f;


CRACKS!

void Test::calcPNAENIndices(const std::vector<USHORT>& ind, const std::vector<VERTEX>& verts, std::vector<USHORT>& out)
{
out.resize(ind.size() * 3);
for (std::size_t i = 0; i < ind.size(); i += 3)
{
out[3 * i + 0] = ind[i + 0];
out[3 * i + 1] = ind[i + 1];
out[3 * i + 2] = ind[i + 2];

out[3 * i + 3] = ind[i + 0];
out[3 * i + 4] = ind[i + 1];
out[3 * i + 5] = ind[i + 1];

out[3 * i + 6] = ind[i + 2];
out[3 * i + 7] = ind[i + 2];
out[3 * i + 8] = ind[i + 0];
}

struct Edge
{
float3 p[2];
USHORT inx[2];

bool operator == (const Edge& o) const
{
if (inx[0] == o.inx[0] && inx[1] == o.inx[1])
return true;

if (Equal(p[0].x, o.p[0].x) && Equal(p[0].y, o.p[0].y) && Equal(p[0].z, o.p[0].z))
{
if (Equal(p[1].x, o.p[1].x) && Equal(p[1].y, o.p[1].y) && Equal(p[1].z, o.p[1].z))
{
return true;
}
}

return false;
}
};

// reverse edges
std::vector<Edge> edges;
edges.resize(ind.size());
for (std::size_t i = 0; i < ind.size(); i += 3)
{
edges[i + 0].p[1]   = verts[ind[i + 0]].pos;
edges[i + 0].p[0]   = verts[ind[i + 1]].pos;
edges[i + 0].inx[1] = ind[i + 0];
edges[i + 0].inx[0] = ind[i + 1];

edges[i + 1].p[1]   = verts[ind[i + 1]].pos;
edges[i + 1].p[0]   = verts[ind[i + 2]].pos;
edges[i + 1].inx[1] = ind[i + 1];
edges[i + 1].inx[0] = ind[i + 2];

edges[i + 2].p[1]   = verts[ind[i + 2]].pos;
edges[i + 2].p[0]   = verts[ind[i + 0]].pos;
edges[i + 2].inx[1] = ind[i + 2];
edges[i + 2].inx[0] = ind[i + 0];
}

// compare
for (std::size_t i = 0, j = 0; i < out.size(); i += 9, j += 3)
{
Edge e;

// edge 0
e.p[0]   = verts[out[i + 0]].pos;
e.p[1]   = verts[out[i + 1]].pos;
e.inx[0] = out[i + 0];
e.inx[1] = out[i + 1];

if (e == edges[j + 0])
{
out[i + 0] = edges[j + 0].inx[0];
out[i + 1] = edges[j + 0].inx[1];
}

// edge 1
e.p[0]   = verts[out[i + 1]].pos;
e.p[1]   = verts[out[i + 2]].pos;
e.inx[0] = out[i + 1];
e.inx[1] = out[i + 2];

if (e == edges[j + 0])
{
out[i + 1] = edges[j + 0].inx[0];
out[i + 2] = edges[j + 0].inx[1];
}

// edge 2
e.p[0]   = verts[out[i + 2]].pos;
e.p[1]   = verts[out[i + 3]].pos;
e.inx[0] = out[i + 2];
e.inx[1] = out[i + 3];

if (e == edges[j + 0])
{
out[i + 2] = edges[j + 0].inx[0];
out[i + 3] = edges[j + 0].inx[1];
}

// edge 3
e.p[0] = verts[out[i + 3]].pos;
e.p[1] = verts[out[i + 4]].pos;
e.inx[0] = out[i + 3];
e.inx[1] = out[i + 4];

if (e == edges[j + 1])
{
out[i + 3] = edges[j + 1].inx[0];
out[i + 4] = edges[j + 1].inx[1];
}

// edge 4
e.p[0] = verts[out[i + 4]].pos;
e.p[1] = verts[out[i + 5]].pos;
e.inx[0] = out[i + 4];
e.inx[1] = out[i + 5];

if (e == edges[j + 1])
{
out[i + 4] = edges[j + 1].inx[0];
out[i + 5] = edges[j + 1].inx[1];
}

// edge 5
e.p[0] = verts[out[i + 5]].pos;
e.p[1] = verts[out[i + 6]].pos;
e.inx[0] = out[i + 5];
e.inx[1] = out[i + 6];

if (e == edges[j + 1])
{
out[i + 5] = edges[j + 1].inx[0];
out[i + 6] = edges[j + 1].inx[1];
}

// edge 6
e.p[0] = verts[out[i + 6]].pos;
e.p[1] = verts[out[i + 7]].pos;
e.inx[0] = out[i + 6];
e.inx[1] = out[i + 7];

if (e == edges[j + 2])
{
out[i + 6] = edges[j + 2].inx[0];
out[i + 7] = edges[j + 2].inx[1];
}

// edge 7
e.p[0]   = verts[out[i + 7]].pos;
e.p[1]   = verts[out[i + 8]].pos;
e.inx[0] = out[i + 7];
e.inx[1] = out[i + 8];

if (e == edges[j + 2])
{
out[i + 7] = edges[j + 2].inx[0];
out[i + 8] = edges[j + 2].inx[1];
}

// edge 8
e.p[0] = verts[out[i + 8]].pos;
e.p[1] = verts[out[i + 0]].pos;
e.inx[0] = out[i + 8];
e.inx[1] = out[i + 0];

if (e == edges[j + 2])
{
out[i + 8] = edges[j + 2].inx[0];
out[i + 0] = edges[j + 2].inx[1];
}
}
}


Edited by belfegor, 27 June 2014 - 09:39 AM.

### #6MJP  Moderators   -  Reputation: 11038

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Posted 27 June 2014 - 04:11 PM

I don't suppose there's any video / audio recording of the presentation using those slides available somewhere, possibly for a nominal fee?

Not that I know of, sorry.

On a more off-topic note, I recognize that avatar of yours but have been unable to remember the name of the show (or was it possibly a book?) it featured in, care to enlighten me?

It's Rocko!

### #7belfegor  Crossbones+   -  Reputation: 2575

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Posted 28 June 2014 - 04:46 PM

I think i had some mistakes in code, having hard time to understand what exactly i need to do.

Here is corrected version but still wrong results.

void Test::calcPNAENIndices(const std::vector<USHORT>& ind, const std::vector<VERTEX>& verts, std::vector<USHORT>& out)
{
struct Edge
{
float3 p[2];
USHORT inx[2];

bool operator == (const Edge& o) const
{
if (inx[0] == o.inx[0] && inx[1] == o.inx[1])
return true;

if (Equal(p[0].x, o.p[0].x) && Equal(p[0].y, o.p[0].y) && Equal(p[0].z, o.p[0].z))
{
if (Equal(p[1].x, o.p[1].x) && Equal(p[1].y, o.p[1].y) && Equal(p[1].z, o.p[1].z))
{
return true;
}
}

return false;
}
};

std::vector<Edge> edges(ind.size());
out.resize(ind.size() * 3);

for (std::size_t i = 0; i < ind.size(); i += 3)
{
// initial values
out[3 * i + 0] = ind[i + 0];
out[3 * i + 1] = ind[i + 1];
out[3 * i + 2] = ind[i + 2];

out[3 * i + 3] = ind[i + 0];
out[3 * i + 4] = ind[i + 1];
out[3 * i + 5] = ind[i + 1];

out[3 * i + 6] = ind[i + 2];
out[3 * i + 7] = ind[i + 2];
out[3 * i + 8] = ind[i + 0];

// store reversed
edges[i + 0].p[1]   = verts[ind[i + 0]].pos;
edges[i + 0].p[0]   = verts[ind[i + 1]].pos;
edges[i + 0].inx[1] = ind[i + 0];
edges[i + 0].inx[0] = ind[i + 1];

edges[i + 1].p[1]   = verts[ind[i + 1]].pos;
edges[i + 1].p[0]   = verts[ind[i + 2]].pos;
edges[i + 1].inx[1] = ind[i + 1];
edges[i + 1].inx[0] = ind[i + 2];

edges[i + 2].p[1]   = verts[ind[i + 2]].pos;
edges[i + 2].p[0]   = verts[ind[i + 0]].pos;
edges[i + 2].inx[1] = ind[i + 2];
edges[i + 2].inx[0] = ind[i + 0];
}

for (std::size_t i = 0; i < out.size(); i += 9)
{
// i think i should skip first 3 indices as they point to triangle and i need to check edges
for (std::size_t j = 3; j < 9; ++j)
{
std::size_t first  = j;
std::size_t second = j + 1;
if (second == 9)
second = 3;

Edge e;
e.p[0]   = verts[out[i + first]].pos;
e.p[1]   = verts[out[i + second]].pos;
e.inx[0] = out[i + first];
e.inx[1] = out[i + second];

for (std::size_t k = 0; k < edges.size(); ++k)
{
if (e == edges[k])
{
out[i + first]  = edges[k].inx[0];
out[i + second] = edges[k].inx[1];
}
}
}
}
}


Can someone take a look please and decipher instructions given for this to work:

1.  Create an output IB that is 3 times the size of input IB.

2.  For each input Triangle in IB, with indices i0, i1 and i2:
a.  Write out an initial output entry of:  i0, i1, i2, i0, i1, i1, i2, i2, i0, which sets edges to

initially be neighbors of themselves. This would produce identical results to PN
Triangles.
b.  Lookup the positions p0, p1, and p2, using i0, i1 and i2 to perform a lookup for
position of the associated vertex in VB.
c.  Define 3 Edges, which consist of the two indices and two positions that make up
the corresponding Edge. An Edge should consist of the origin index, the
destination index, the origin position and the destination position.
d.  For each edge, store the reverse of that edge in an easily searchable data structure
for the next step. The reference implementation uses an stdext::hash_map<Edge,
Edge> for this purpose. Reverse simply flips the sense of the edge (originating at
the destination position and index and heading to the origin position and index).

3.  Walk the output index buffer (OB) constructed in step 2. For each patch of 9 indices:
a.  For each Edge in the current Patch, perform a lookup into Edge->Edge mapping
created in step 2d.
b.  If found, replace the current indices with the indices found in the map. Note that
two edges should be considered matching if their "from" and "to" indices match,
OR if their "from" and "to" positions match.
c.  If not, continue to use the existing indices.

Upon completion of this algorithm, a buffer suitable for usage with PN-AEN will be
available.

Edited by belfegor, 28 June 2014 - 04:48 PM.

### #8unbird  Crossbones+   -  Reputation: 4973

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Posted 28 June 2014 - 07:01 PM

Ah, the art and joy of dissecting papers. I would have had it yesterday if I did not stumble about a silly bug in the vertex shader.

First, I can give you a handy test case: Two triangles sharing an edge. With some funny normals.

Wavefront mesh:
o FlappyTriangles
v -2 0 0.5
v 0 1 0
v 0 -1 0
v 0 -1 0
v 0 1 0
v 2 0 0.5
n -0.4472136 0 -0.8944272
n -0.09950372 0 -0.9950371
n -0.4454354 0.08908708 -0.8908708
n 0.4402255 -0.1760902 -0.8804509
n 0.09950372 0 -0.9950371
n 0.5734624 0 -0.8192319
f 1 2 3
f 4 5 6

Original indices (simple):
0,1,2,3,4,5

Initial PNAEN indices:
0,1,2,0,1,1,2,2,0,3,4,5,3,4,4,5,5,3

These are the edges that should be replaced:
edge ([2->1]:(X:0 Y:-1 Z:0;X:0 Y:1 Z:0)) replaced with ([4->3]:(X:0 Y:1 Z:0;X:0 Y:-1 Z:0))
edge ([4->3]:(X:0 Y:1 Z:0;X:0 Y:-1 Z:0)) replaced with ([2->1]:(X:0 Y:-1 Z:0;X:0 Y:1 Z:0))

So, the corrected PNAEN indices are:
0,1,2,0,1,4,3,2,0,3,4,5,2,1,4,5,5,3

You're close. Yes, only replace edges from the "extension", not from the inner triangle.
Couple of things I noticed:
• You need to search for the flipped edge.
• Minor problem: Your inner loop should increment by 2, since an edge has two points. Probably not a problem, I guess you won't find those edges anyway since they are degenerate (identical positions)
• You can also break the search loop once you found the edge. Or use a map as suggested
This is the code that worked for me (C# but I think you get the idea):
for (int i = 3; i < pnaenIndices.Count; i += 9)
{
for (int k = 0; k < 6; k += 2)
{
var i0 = pnaenIndices[i + k];
var i1 = pnaenIndices[i + k + 1];
var edge = generateEdge(i1, i0); // Note: Flipped !!!
PNAENEdge replaceEdge;
if (map.TryGetValue(edge, out replaceEdge))
{
pnaenIndices[i + k] = replaceEdge.Index1;
pnaenIndices[i + k + 1] = replaceEdge.Index2;
}
}
}

Below two screenshots, first usual PN triangles showing cracks, the second PNAEN without

PS: The bug in the vertex shader is that the normals don't get normalized. This screws the subsequent control point calculation badly if you got any scaling going on

### #9belfegor  Crossbones+   -  Reputation: 2575

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Posted 29 June 2014 - 12:16 AM

That is that. Thank you very much.

With "initial" IB (notice cracks):

PNAEN

Now i would like to displace position along normal using heightmap but i dont know how to get average normal so i can pass it to domain shader. Any pointers?

### #10unbird  Crossbones+   -  Reputation: 4973

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Posted 01 July 2014 - 02:53 AM

Now the real challenge starts. Here the sample goes the easy way and just passes the normals from the inner triangle and interpolates linearly. "Correct" PN triangles uses a quadratic bezier patch for the normals, examples of which you can find in the (June 2010 SDK) samples or in the Hieroglyph 3 engine (there's also full chapter in the Practical Rendering book).
There's also a displacement tesselation sample using decals in the SDK which might be worth a peek.

Either way it sounds complex as the presentation MJP linked to shows. Can't help you any further now, I haven't done displacement mapping (not counting terrain). For a simple start maybe you can get away averaging normals at corners (not using a bezier quad patch and taking averaged normals from all adjacent triangles). But that's really just an idea.

Anyway, looks like it also needs special care on the content creation side (citing above presentation).

Speaking of which (and out of curiosity): Why does that pig/boar generate cracks ? I wouldn't expect them on organic surfaces (the initial index buffer results in usual PN triangles). You got a link to that mesh ?

### #11Husbjörn  Members   -  Reputation: 243

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Posted 28 July 2014 - 05:55 AM

It's Rocko!

Ah yes, haha, remember watching that in the mid-late 90's. Maybe worth a rewatch now that I'm old enough to actually understand it better than back then...

As for the displacement mapping I eventually settled on a rather simple approach for use with pre-existing triangle list meshes (it is by no means perfect but it seems that the "real" solution is really just having the 3D / texturing artist(s) being aware of your intents and have them author appropriately mapped bump maps and ensure corners actually are rounded, albeit with extremely short edges between corner vertices, as seemed to be the main point that the chapter in Zink, Pettineo & Hoxley (2011) as referred by unbird in the last post). Basically I average all disjoint vertex normals and create a 6-control patch index buffer that holds the initial triangle in the first 3 indices and then any "dominant" vertices sharing the position of these original vertices in the last 3 indices. The dominant vertices are arbitrarily chosen as the first found in the vertex data for a given position and are set to the same vertex as in the first three indices if there are no shared vertices at a given position. The dominant vertex is used to ensure that all overlapping vertices will sample the same value from the displacement map, while still allowing them to sample other textures by their UV coords.

Not perfect but good enough for some general-purpose examples.

As for actually employing this kind of displacement mapping in a more professional game / visual demo / what-have-you, the artist should ensure that there are *no* disjoint vertices (as said, such vertices can be moved slightly apart and be connected by a short edge, allowing the corners to appear mostly sharp) and a secondary set of texture coordinates should be provided for the displacement map / alternatively the displacement map should be handcrafted such that when displaced (with a reasonable strength / height factor), faces won't extrude through each others.

Of course there exists more elaborate ways as described in the previous posts, I just thought I would share this if anyone found it interesting, After tracking down a copy of that practical rendering book just for that tessellation chapter, it didn't say that much more about this particular problem, so might as well save others the trouble.

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