GLSL shader generation of normals - optimization

Hi I am writing 3D modeling app and I want to speed up rendering in OpenGL. Currently I use glBegin/glEnd which is really slow and deprecated way. I need to draw very fast flat shaded models. I generate normals on CPU every single frame. This is very slow. I tried to use glDrawElements with indexed geometry, but there is problem in normal generation, because normals are specified at vertex not at triangle level.
Another idea was to use GLSL to generate normals on GPU in geometry shader. I written this code for normal generation:
#version 120
#extension GL_EXT_geometry_shader4 : enable
vec3 NormalFromTriangleVertices(vec3 triangleVertices[3])
{
// now is same as RedBook (OpenGL Programming Guide)
vec3 u = triangleVertices[0] - triangleVertices[1];
vec3 v = triangleVertices[1] - triangleVertices[2];
return cross(v, u);
}
void main()
{
// no change of position
// computes normal from input triangle and front color for that triangle
vec3 triangleVertices[3];
vec3 computedNormal;
vec3 normal, lightDir;
vec4 diffuse;
float NdotL;
vec4 finalColor;
for(int i = 0; i < gl_VerticesIn; i += 3)
{
for (int j = 0; j < 3; j++)
{
triangleVertices[j] = gl_PositionIn[i + j].xyz;
}
computedNormal = NormalFromTriangleVertices(triangleVertices);
normal = normalize(gl_NormalMatrix * computedNormal);
// hardcoded light direction
vec4 light = gl_ModelViewMatrix * vec4(0.0, 0.0, 1.0, 0.0);
lightDir = normalize(light.xyz);
NdotL = max(dot(normal, lightDir), 0.0);
// hardcoded
diffuse = vec4(0.5, 0.5, 0.9, 1.0);
finalColor = NdotL * diffuse;
finalColor.a = 1.0; // final color ignores everything, except lighting
for (int j = 0; j < 3; j++)
{
gl_FrontColor = finalColor;
gl_Position = gl_PositionIn[i + j];
EmitVertex();
}
}
EndPrimitive();
}
When I integrated shaders to my application, no speed improvement occurred. It was worse than before. I am newbie in GLSL and shaders overall so I don't know what I done wrong.
I tried this code on MacBook with Geforce 9400M.
To be more clear, this is code I want to replace:
- (void)drawAsCommandsWithScale:(Vector3D)scale
{
float frontDiffuse[4] = { 0.4, 0.4, 0.4, 1 };
CGFloat components[4];
[color getComponents:components];
float backDiffuse[4];
float selectedDiffuse[4] = { 1.0f, 0.0f, 0.0f, 1 };
for (uint i = 0; i < 4; i++)
backDiffuse[i] = components[i];
glMaterialfv(GL_BACK, GL_DIFFUSE, backDiffuse);
glMaterialfv(GL_FRONT, GL_DIFFUSE, frontDiffuse);
Vector3D triangleVertices[3];
float *lastDiffuse = frontDiffuse;
BOOL flip = scale.x < 0.0f || scale.y < 0.0f || scale.z < 0.0f;
glBegin(GL_TRIANGLES);
for (uint i = 0; i < triangles->size(); i++)
{
if (selectionMode == MeshSelectionModeTriangles)
{
if (selected->at(i))
{
if (lastDiffuse == frontDiffuse)
{
glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, selectedDiffuse);
lastDiffuse = selectedDiffuse;
}
}
else if (lastDiffuse == selectedDiffuse)
{
glMaterialfv(GL_BACK, GL_DIFFUSE, backDiffuse);
glMaterialfv(GL_FRONT, GL_DIFFUSE, frontDiffuse);
lastDiffuse = frontDiffuse;
}
}
Triangle currentTriangle = [self triangleAtIndex:i];
if (flip)
currentTriangle = FlipTriangle(currentTriangle);
[self getTriangleVertices:triangleVertices fromTriangle:currentTriangle];
for (uint j = 0; j < 3; j++)
{
for (uint k = 0; k < 3; k++)
{
triangleVertices[j][k] *= scale[k];
}
}
Vector3D n = NormalFromTriangleVertices(triangleVertices);
n.Normalize();
for (uint j = 0; j < 3; j++)
{
glNormal3f(n.x, n.y, n.z);
glVertex3f(triangleVertices[j].x, triangleVertices[j].y, triangleVertices[j].z);
}
}
glEnd();
}
As you can see it is very inefficient, but working.triangles is array of indexes into vertices array.
I tried to use this code for drawing, but I can't have only one index array not two (one for vertices and second for normals).
glEnableClientState(GL_VERTEX_ARRAY);
uint *trianglePtr = (uint *)(&(*triangles)[0]);
float *vertexPtr = (float *)(&(*vertices)[0]);
glVertexPointer(3, GL_FLOAT, 0, vertexPtr);
glDrawElements(GL_TRIANGLES, triangles->size() * 3, GL_UNSIGNED_INT, trianglePtr);
glDisableClientState(GL_VERTEX_ARRAY);
Now, how can I specify pointer to normals, when some vertices are shared by different triangles, so different normals for them?

So I finally managed to increase rendering speed. I recalculate normals on CPU, only when vertices or triangles changes, which occurs only when working in one mesh not in whole scene.
It is not solution that I wanted but in real world it is better than previous approaches.
I cache whole geometry into separate normal and vertex array, indexed drawing cannot be used because I want flat shading (similar problem to smoothing groups in 3ds max).
I use simple glDrawArrays and for lighting vertex shader, that is because I want in triangle mode different color for selected triangle and another one for unselected and there is no array of materials (I didn't found any one).

You wouldn't usually calculate the normals every frame, only when the geometry changes.
And to have one normal per triangle just set the same normal for each vertex in the triangle. That does mean you can't share vertices between adjacent triangles in your mesh but that's not unusual at all in this kind of thing.

Your question makes me remember this Normals without Normals blog post.

Related

Skeletal animation bug with Assimp in DirectX 12

I am using Assimp to load an FBX model with animation (created in Blender) into my DirectX 12 game, but I'm experiencing a very frustrating bug with the animation rendered by the game application.
The test model is a simple 'flagpole' containing four bones like so:
Bone0 -> Bone1 -> Bone2 -> Bone3
The model renders correctly in its rest pose when the keyframe animation is bypassed.
The model also renders and animates properly when the animation rotates the model only by the root bone (Bone0).
However, when importing a model that rotates at the first joint (i.e. at Bone1), the vertices clustered around each joint seem 'stuck' in their original positions, while the vertices surrounding the 'bones' proper appear to follow through with the correct animation.
The result is a crappy zigzag of stretched geometry like so:
Instead the model should resemble an 'allen-key' shape at the end of its animation pose, as shown by the same model rendered in the AssimpViewer utility tool:
Since the model is rendering correctly in AssimpViewer, it's reasonable to assume there are no issues with the FBX file exported by Blender. I then checked and confirmed that the vertices 'stuck' around the joints did indeed have their vertex weights correctly assigned by the game loading code.
The C++ model loading and animation code is based on the popular OGLDev tutorial: https://ogldev.org/www/tutorial38/tutorial38.html
Now the infuriating thing is, since the AssimpViewer tool was correctly rendering the model animation, I also copied in the SceneAnimator and AnimEvaluator classes from that tool to generate the final bone transforms via that code branch as well... only to end up with exactly the same zigzag bug in the game!
I'm reasonably confident there aren't any issues with finding the bone hierarchy structure at initialization, so here are the key functions that traverse the hierarchy and interpolate key frames each frame.
VOID Mesh::ReadNodeHeirarchy(FLOAT animationTime, CONST aiNode* pNode, CONST aiAnimation* pAnim, CONST aiMatrix4x4 parentTransform)
{
std::string nodeName(pNode->mName.data);
// nodeTransform is a relative transform to parent node space
aiMatrix4x4 nodeTransform = pNode->mTransformation;
CONST aiNodeAnim* pNodeAnim = FindNodeAnim(pAnim, nodeName);
if (pNodeAnim)
{
// Interpolate scaling and generate scaling transformation matrix
aiVector3D scaling(1.f, 1.f, 1.f);
CalcInterpolatedScaling(scaling, animationTime, pNodeAnim);
// Interpolate rotation and generate rotation transformation matrix
aiQuaternion rotationQ (1.f, 0.f, 0.f, 0.f);
CalcInterpolatedRotation(rotationQ, animationTime, pNodeAnim);
// Interpolate translation and generate translation transformation matrix
aiVector3D translat(0.f, 0.f, 0.f);
CalcInterpolatedPosition(translat, animationTime, pNodeAnim);
// build the SRT transform matrix
nodeTransform = aiMatrix4x4(rotationQ.GetMatrix());
nodeTransform.a1 *= scaling.x; nodeTransform.b1 *= scaling.x; nodeTransform.c1 *= scaling.x;
nodeTransform.a2 *= scaling.y; nodeTransform.b2 *= scaling.y; nodeTransform.c2 *= scaling.y;
nodeTransform.a3 *= scaling.z; nodeTransform.b3 *= scaling.z; nodeTransform.c3 *= scaling.z;
nodeTransform.a4 = translat.x; nodeTransform.b4 = translat.y; nodeTransform.c4 = translat.z;
}
aiMatrix4x4 globalTransform = parentTransform * nodeTransform;
if (m_boneMapping.find(nodeName) != m_boneMapping.end())
{
UINT boneIndex = m_boneMapping[nodeName];
// the global inverse transform returns us to mesh space!!!
m_boneInfo[boneIndex].FinalTransform = m_globalInverseTransform * globalTransform * m_boneInfo[boneIndex].BoneOffset;
//m_boneInfo[boneIndex].FinalTransform = m_boneInfo[boneIndex].BoneOffset * globalTransform * m_globalInverseTransform;
m_shaderTransforms[boneIndex] = aiMatrixToSimpleMatrix(m_boneInfo[boneIndex].FinalTransform);
}
for (UINT i = 0u; i < pNode->mNumChildren; i++)
{
ReadNodeHeirarchy(animationTime, pNode->mChildren[i], pAnim, globalTransform);
}
}
VOID Mesh::CalcInterpolatedRotation(aiQuaternion& out, FLOAT animationTime, CONST aiNodeAnim* pNodeAnim)
{
UINT rotationKeys = pNodeAnim->mNumRotationKeys;
// we need at least two values to interpolate...
if (rotationKeys == 1u)
{
CONST aiQuaternion& key = pNodeAnim->mRotationKeys[0u].mValue;
out = key;
return;
}
UINT rotationIndex = FindRotation(animationTime, pNodeAnim);
UINT nextRotationIndex = (rotationIndex + 1u) % rotationKeys;
assert(nextRotationIndex < rotationKeys);
CONST aiQuatKey& key = pNodeAnim->mRotationKeys[rotationIndex];
CONST aiQuatKey& nextKey = pNodeAnim->mRotationKeys[nextRotationIndex];
FLOAT deltaTime = FLOAT(nextKey.mTime) - FLOAT(key.mTime);
FLOAT factor = (animationTime - FLOAT(key.mTime)) / deltaTime;
assert(factor >= 0.f && factor <= 1.f);
aiQuaternion::Interpolate(out, key.mValue, nextKey.mValue, factor);
}
I've just included the rotation interpolation here, since the scaling and translation functions are identical. For those unaware, Assimp's aiMatrix4x4 type follows a column-vector math convention, so I haven't messed with original matrix multiplication order.
About the only deviation between my code and the two Assimp-based code branches I've adopted is the requirement to convert the final transforms from aiMatrix4x4 types into a DirectXTK SimpleMath Matrix (really an XMMATRIX) with this conversion function:
Matrix Mesh::aiMatrixToSimpleMatrix(CONST aiMatrix4x4 m)
{
return Matrix
(m.a1, m.a2, m.a3, m.a4,
m.b1, m.b2, m.b3, m.b4,
m.c1, m.c2, m.c3, m.c4,
m.d1, m.d2, m.d3, m.d4);
}
Because of the column-vector orientation of aiMatrix4x4 Assimp matrices, the final bone transforms are not transposed for HLSL consumption. The array of final bone transforms are passed to the skinning vertex shader constant buffer as follows.
commandList->SetPipelineState(m_psoForwardSkinned.Get()); // set PSO
// Update vertex shader with current bone transforms
CONST std::vector<Matrix> transforms = m_assimpModel.GetShaderTransforms();
VSBonePassConstants vsBoneConstants{};
for (UINT i = 0; i < m_assimpModel.GetNumBones(); i++)
{
// We do not transpose bone matrices for HLSL because the original
// Assimp matrices are column-vector matrices.
vsBoneConstants.boneTransforms[i] = transforms[i];
//vsBoneConstants.boneTransforms[i] = transforms[i].Transpose();
//vsBoneConstants.boneTransforms[i] = Matrix::Identity;
}
GraphicsResource vsBoneCB = m_graphicsMemory->AllocateConstant(vsBoneConstants);
vsPerObjects.gWorld = m_assimp_world.Transpose(); // vertex shader per object constant
vsPerObjectCB = m_graphicsMemory->AllocateConstant(vsPerObjects);
commandList->SetGraphicsRootConstantBufferView(RootParameterIndex::VSBoneConstantBuffer, vsBoneCB.GpuAddress());
commandList->SetGraphicsRootConstantBufferView(RootParameterIndex::VSPerObjConstBuffer, vsPerObjectCB.GpuAddress());
//commandList->SetGraphicsRootDescriptorTable(RootParameterIndex::ObjectSRV, m_shaderTextureHeap->GetGpuHandle(ShaderTexDescriptors::SuzanneDiffuse));
commandList->SetGraphicsRootDescriptorTable(RootParameterIndex::ObjectSRV, m_shaderTextureHeap->GetGpuHandle(ShaderTexDescriptors::DefaultDiffuse));
for (UINT i = 0; i < m_assimpModel.GetMeshSize(); i++)
{
commandList->IASetVertexBuffers(0u, 1u, &m_assimpModel.meshEntries[i].GetVertexBufferView());
commandList->IASetIndexBuffer(&m_assimpModel.meshEntries[i].GetIndexBufferView());
commandList->IASetPrimitiveTopology(D3D_PRIMITIVE_TOPOLOGY_TRIANGLELIST);
commandList->DrawIndexedInstanced(m_assimpModel.meshEntries[i].GetIndexCount(), 1u, 0u, 0u, 0u);
}
Please note I am using the Graphics Resource memory management helper object found in the DirectXTK12 library in the code above. Finally, here's the skinning vertex shader I'm using.
// Luna (2016) lighting model adapted from Moller
#define MAX_BONES 4
// vertex shader constant data that varies per object
cbuffer cbVSPerObject : register(b3)
{
float4x4 gWorld;
//float4x4 gTexTransform;
}
// vertex shader constant data that varies per frame
cbuffer cbVSPerFrame : register(b5)
{
float4x4 gViewProj;
float4x4 gShadowTransform;
}
// bone matrix constant data that varies per object
cbuffer cbVSBonesPerObject : register(b9)
{
float4x4 gBoneTransforms[MAX_BONES];
}
struct VertexIn
{
float3 posL : SV_POSITION;
float3 normalL : NORMAL;
float2 texCoord : TEXCOORD0;
float3 tangentU : TANGENT;
float4 boneWeights : BONEWEIGHT;
uint4 boneIndices : BONEINDEX;
};
struct VertexOut
{
float4 posH : SV_POSITION;
//float3 posW : POSITION;
float4 shadowPosH : POSITION0;
float3 posW : POSITION1;
float3 normalW : NORMAL;
float2 texCoord : TEXCOORD0;
float3 tangentW : TANGENT;
};
VertexOut VS_main(VertexIn vin)
{
VertexOut vout = (VertexOut)0.f;
// Perform vertex skinning.
// Ignore BoneWeights.w and instead calculate the last weight value
// to ensure all bone weights sum to unity.
float4 weights = vin.boneWeights;
//weights.w = 1.f - dot(weights.xyz, float3(1.f, 1.f, 1.f));
//float4 weights = { 0.f, 0.f, 0.f, 0.f };
//weights.x = vin.boneWeights.x;
//weights.y = vin.boneWeights.y;
//weights.z = vin.boneWeights.z;
weights.w = 1.f - (weights.x + weights.y + weights.z);
float4 localPos = float4(vin.posL, 1.f);
float3 localNrm = vin.normalL;
float3 localTan = vin.tangentU;
float3 objPos = mul(localPos, (float4x3)gBoneTransforms[vin.boneIndices.x]).xyz * weights.x;
objPos += mul(localPos, (float4x3)gBoneTransforms[vin.boneIndices.y]).xyz * weights.y;
objPos += mul(localPos, (float4x3)gBoneTransforms[vin.boneIndices.z]).xyz * weights.z;
objPos += mul(localPos, (float4x3)gBoneTransforms[vin.boneIndices.w]).xyz * weights.w;
float3 objNrm = mul(localNrm, (float3x3)gBoneTransforms[vin.boneIndices.x]) * weights.x;
objNrm += mul(localNrm, (float3x3)gBoneTransforms[vin.boneIndices.y]) * weights.y;
objNrm += mul(localNrm, (float3x3)gBoneTransforms[vin.boneIndices.z]) * weights.z;
objNrm += mul(localNrm, (float3x3)gBoneTransforms[vin.boneIndices.w]) * weights.w;
float3 objTan = mul(localTan, (float3x3)gBoneTransforms[vin.boneIndices.x]) * weights.x;
objTan += mul(localTan, (float3x3)gBoneTransforms[vin.boneIndices.y]) * weights.y;
objTan += mul(localTan, (float3x3)gBoneTransforms[vin.boneIndices.z]) * weights.z;
objTan += mul(localTan, (float3x3)gBoneTransforms[vin.boneIndices.w]) * weights.w;
vin.posL = objPos;
vin.normalL = objNrm;
vin.tangentU.xyz = objTan;
//vin.posL = posL;
//vin.normalL = normalL;
//vin.tangentU.xyz = tangentL;
// End vertex skinning
// transform to world space
float4 posW = mul(float4(vin.posL, 1.f), gWorld);
vout.posW = posW.xyz;
// assumes nonuniform scaling, otherwise needs inverse-transpose of world matrix
vout.normalW = mul(vin.normalL, (float3x3)gWorld);
vout.tangentW = mul(vin.tangentU, (float3x3)gWorld);
// transform to homogenous clip space
vout.posH = mul(posW, gViewProj);
// pass texcoords to pixel shader
vout.texCoord = vin.texCoord;
//float4 texC = mul(float4(vin.TexC, 0.0f, 1.0f), gTexTransform);
//vout.TexC = mul(texC, gMatTransform).xy;
// generate projective tex-coords to project shadow map onto scene
vout.shadowPosH = mul(posW, gShadowTransform);
return vout;
}
Some last tests I tried before posting:
I tested the code with a Collada (DAE) model exported from Blender, only to observe the same distorted zigzagging in the Win32 desktop application.
I also confirmed the aiScene object for the loaded model returns an identity matrix for the global root transform (also verified in AssimpViewer).
I have stared at this code for about a week and am going out of my mind! Really hoping someone can spot what I have missed. If you need more code or info, please ask!
This seems to be a bug with the published code in the tutorials / documentation. It would be great if you could open an issue-report here: Assimp-Projectpage on GitHub .
It's taken almost another two weeks of pain, but I finally found the bug. It was in my own code, and it was self-inflicted. Before I show the solution, I should explain the further troubleshooting I did to get there.
After losing faith with Assimp (even though the AssimpViewer tool was animating my model correctly), I turned to the FBX SDK. The FBX ViewScene command line utility tool that's available as part of the SDK was also showing and animating my model properly, so I had hope...
So after a few days reviewing the FBX SDK tutorials, and taking another week to write an FBX importer for my Windows desktop game, I loaded my model and... saw exactly the same zig-zag animation anomaly as the version loaded by Assimp!
This frustrating outcome meant I could at least eliminate Assimp and the FBX SDK as the source of the problem, and focus again on the vertex shader. The shader I'm using for vertex skinning was adopted from the 'Character Animation' chapter of Frank Luna's text. It was identical in every way, which led me to recheck the C++ vertex structure declared on the application side...
Here's the C++ vertex declaration for skinned vertices:
struct Vertex
{
// added constructors
Vertex() = default;
Vertex(FLOAT x, FLOAT y, FLOAT z,
FLOAT nx, FLOAT ny, FLOAT nz,
FLOAT u, FLOAT v,
FLOAT tx, FLOAT ty, FLOAT tz) :
Pos(x, y, z),
Normal(nx, ny, nz),
TexC(u, v),
Tangent(tx, ty, tz) {}
Vertex(DirectX::SimpleMath::Vector3 pos,
DirectX::SimpleMath::Vector3 normal,
DirectX::SimpleMath::Vector2 texC,
DirectX::SimpleMath::Vector3 tangent) :
Pos(pos), Normal(normal), TexC(texC), Tangent(tangent) {}
DirectX::SimpleMath::Vector3 Pos;
DirectX::SimpleMath::Vector3 Normal;
DirectX::SimpleMath::Vector2 TexC;
DirectX::SimpleMath::Vector3 Tangent;
FLOAT BoneWeights[4];
BYTE BoneIndices[4];
//UINT BoneIndices[4]; <--- YOU HAVE CAUSED ME A MONTH OF PAIN
};
Quite early on, being confused by Luna's use of BYTE to store the array of bone indices, I changed this structure element to UINT, figuring this still matched the input declaration shown here:
static CONST D3D12_INPUT_ELEMENT_DESC inputElementDescSkinned[] =
{
{ "SV_POSITION", 0u, DXGI_FORMAT_R32G32B32_FLOAT, 0u, D3D12_APPEND_ALIGNED_ELEMENT, D3D12_INPUT_CLASSIFICATION_PER_VERTEX_DATA, 0u },
{ "NORMAL", 0u, DXGI_FORMAT_R32G32B32_FLOAT, 0u, D3D12_APPEND_ALIGNED_ELEMENT, D3D12_INPUT_CLASSIFICATION_PER_VERTEX_DATA, 0u },
{ "TEXCOORD", 0u, DXGI_FORMAT_R32G32_FLOAT, 0u, D3D12_APPEND_ALIGNED_ELEMENT, D3D12_INPUT_CLASSIFICATION_PER_VERTEX_DATA, 0u },
{ "TANGENT", 0u, DXGI_FORMAT_R32G32B32_FLOAT, 0u, D3D12_APPEND_ALIGNED_ELEMENT, D3D12_INPUT_CLASSIFICATION_PER_VERTEX_DATA, 0u },
//{ "BINORMAL", 0, DXGI_FORMAT_R32G32B32_FLOAT, 0, D3D12_APPEND_ALIGNED_ELEMENT, D3D12_INPUT_CLASSIFICATION_PER_VERTEX_DATA, 0 },
{ "BONEWEIGHT", 0u, DXGI_FORMAT_R32G32B32A32_FLOAT, 0u, D3D12_APPEND_ALIGNED_ELEMENT, D3D12_INPUT_CLASSIFICATION_PER_VERTEX_DATA, 0u },
{ "BONEINDEX", 0u, DXGI_FORMAT_R8G8B8A8_UINT, 0u, D3D12_APPEND_ALIGNED_ELEMENT, D3D12_INPUT_CLASSIFICATION_PER_VERTEX_DATA, 0u },
};
Here was the bug. By declaring UINT in the vertex structure for bone indices, four bytes were being assigned to store each bone index. But in the vertex input declaration, the DXGI_FORMAT_R8G8B8A8_UINT format specified for the "BONEINDEX" was assigning one byte per index. I suspect this data type and format size mismatch was resulting in only one valid bone index being able to fit in the BONEINDEX element, and so only one index value was passed to the vertex shader each frame, instead of the whole array of four indices for correct bone transform lookups.
So now I've learned... the hard way... why Luna had declared an array of BYTE for bone indices in the original C++ vertex structure.
I hope this experience will be of value to someone else, and always be careful changing code from your original learning sources.

calculating forward kinematics using D-H matrix

I have a 6-DOF robot arm model:
robot arm structure
I want to calculate forward kinematics, so I uses the D-H matrix. the D-H parameters are:
static const std::vector<float> theta = {
0,0,90.0f,0,-90.0f,0};
// d
static const std::vector<float> d = {
380.948f,0,0,-560.18f,0,0};
// a
static const std::vector<float> a = {
-220.0f,522.331f,80.0f,0,0,94.77f};
// alpha
static const std::vector<float> alpha = {
90.0f,0,90.0f,-90.0f,-90.0f,0};
and the calculation :
glm::mat4 Robothand::armForKinematics() noexcept
{
glm::mat4 pose(1.0f);
float cos_theta, sin_theta, cos_alpha, sin_alpha;
for (auto i = 0; i < 6;i++)
{
cos_theta = cosf(glm::radians(theta[i]));
sin_theta = sinf(glm::radians(theta[i]));
cos_alpha = cosf(glm::radians(alpha[i]));
sin_alpha = sinf(glm::radians(alpha[i]));
glm::mat4 Ai = {
cos_theta, -sin_theta * cos_alpha,sin_theta * sin_alpha, a[i] * cos_theta,
sin_theta, cos_theta * cos_alpha, -cos_theta * sin_alpha,a[i] * sin_theta,
0, sin_alpha, cos_alpha, d[i],
0, 0, 0, 1 };
pose = pose * Ai;
}
return pose;
}
the problem I have is that, I can't get the correct result, for example, I want to calculate the transformation matrix from first joint to the 4th joint, I will change the for loop i < 3,then I can get the pose matrix, and I can the origin coordinate in 4th coordinate system by pose * (0,0,0,1).but the result (380.948,382.331,0) seems not correct because it should be move along x-axis not y-axis. I have read many books and materials about D-H matrix, but I can't figure out what's wrong with it.
I have figured it out by myself, the real problem behind is glm::mat, glm::mat is col-type which means columns will be initialized before rows,I changed the code and get the correct result:
for (int i = 0; i < joint_num; ++i)
{
pose = glm::rotate(pose, glm::radians(degrees[i]), glm::vec3(0, 0, 1));
pose = glm::translate(pose,glm::vec3(0,0,d[i]));
pose = glm::translate(pose, glm::vec3(a[i], 0, 0));
pose = glm::rotate(pose,glm::radians(alpha[i]),glm::vec3(1,0,0));
}
then I can get the position by:
auto pos = pose * glm::vec4(x,y,z,1);

Bidirectional path tracing

I'm making a bidirectional path tracer and I have some troubles.
To be clear :
1) One point light
2) All objects are diffuse
3) All objects are spheres, even walls (they are very large)
4) NO MIS WEIGHTING
The light emission is a 3D vector. The BRDF of a sphere is a 3D vector. Hard coded.
In the main function below I generate EyePath and LightPath then I connect them. At least I try.
In this post I will talking about the main function then EyePath then LightPath. The talking about connecting function will appear once EyePath and Light are good.
First questions :
Does the generation of the first light point is good ?
Do I need to compute this point according to the emission of the light source? or is it just the emission ? The line is commented where i'm filling the Vertices structure.
Do I need to translate fromlight ? In order to put it on the sphere
The code below is sampled in the main function. Above it there is two for loops going through all pixels. Camera.o is the eye. CameraRayDir is the direction to the current pixel.
//The path light starting point is at the same position as the light
Ray fromLight(Vec(0, 24.3, 0), Vec());
Sphere light = spheres[7];
#define PDF 0.15915494309 // 1 / (2 * PI)
for(int i = 0; i < samps; ++i)
{
std::vector<Vertices> PathEye;
std::vector<Vertices> PathLight;
Vec cameraRayDir = cx * (double(x) / w - .5) + cy * (double(y) / h - .5) + camera.d;
Ray rayEye(camera.o, cameraRayDir.norm());
// Hemisphere oriented towards the top
fromLight.d = generateRayInHemisphere(fromLight.o,Vec(0,1,0)).d;
double f = clamp(n.dot(fromLight.d.norm()));
Vertices vert;
vert.d = fromLight.d;
vert.x = fromLight.o;
vert.id = 7;
vert.cos = f;
vert.n = Vec(0,1,0).norm();
// this one ?
//vert.couleur = spheres[7].e * f / PDF;
// Or this one ?
vert.couleur = spheres[7].e;
PathLight.push_back(vert);
int sizeEye = generateEyePath(PathEye, rayEye, maxDepth);
int sizeLight = generateLightPath(PathLight, fromLight, maxDepth);
for (int s = 0; s < sizeLight; ++s)
{
for (int t = 1; t < sizeEye; ++t)
{
int depth = t + s - 1;
if ((s == 0 && t == 0) || depth < 0 || depth > maxDepth)
continue;
pixelValue = pixelValue + connectPaths(PathEye, PathLight, s, t);
}
}
}
For the EyePath I intersect the geometry then I compute the illumination according to the distance with the light. The colour is black if the point is in the shadow.
Second question : For the eye path and the direct illumination, is the computation good ? I've seen in many code, people use the pdf even in direct illumination. But I'm only using point light and spheres.
int generateEyePath(std::vector<Vertices>& v, Ray eye, int maxDepth)
{
double t;
int id = 0;
Vertices vert;
int RussianRoulette;
while(v.size() <= maxDepth)
{
if(distribRREye(generatorRREye) < 10)
break;
// Intersect all the geometry
// id is the id of the intersected geometry in an array
intersect(eye, t, id);
const Sphere& obj = spheres[id];
// Intersection point
Vec x = eye.o + eye.d * t;
// normal
Vec n = (x - obj.p).norm();
Vec direction = light.p - x;
// Shadow ray
Ray RaytoLight = Ray(x, direction.norm());
const float distance = direction.length();
// shadow
const bool visibility = intersect(RaytoLight, t, id);
const Sphere &lumiere = spheres[id];
float degree = clamp(n.dot((lumiere.p - x).norm()));
// If the intersected geometry is not a light, then in shadow
if(lumiere.e.x == 0)
{
vert.couleur = Vec();
}
else // else we compute the colour
// obj.c is the brdf, lumiere.e is the emission
vert.couleur = (obj.c).mult(lumiere.e / (distance * distance)) * degree;
vert.x = x;
vert.id = id;
vert.n = n;
vert.d = eye.d.normn();
vert.cos = degree;
v.push_back(vert);
eye = generateRayInHemisphere(x,n);
}
return v.size();
}
For the LightPath, for a given point, I compute it according to the previous one and the values at this point. Like in a common path tracing.\n
Third question: Is the colour computation good ?
int generateLightPath(std::vector<Vertices>& v, Ray fromLight, int maxDepth)
{
double t;
int id = 0;
Vertices vert;
Vec previous;
while(v.size() <= maxDepth)
{
if(distribRRLight(generatorRRLight) < 10)
break;
previous = v.back().couleur;
intersect(fromLight, t, id);
// intersected geometry
const Sphere& obj = spheres[id];
// Intersection point
Vec x = fromLight.o + fromLight.d * t;
// normal
Vec n = (x - obj.p).norm();
double f = clamp(n.dot(fromLight.d.norm()));
// obj.c is the brdf
vert.couleur = previous.mult(((obj.c / M_PI) * f) / PDF);
vert.x = x;
vert.id = id;
vert.n = n;
vert.d = fromLight.d.norm();
vert.cos = f;
v.push_back(vert);
fromLight = generateRayInHemisphere(x,n);
}
return v.size();
}
For the moment I get this result.
enter image description here
The connecting function will come once EyePath and LightPath are good.
Thank you all
Try the spherical reference scene mentioned in this paper. I think then you can work out most of your questions by yourself since it has an analytical solution.
https://www.researchgate.net/publication/221546261_Testing_Monte-Carlo_Global_Illumination_Methods_with_Analytically_Computable_Scenes
It would save your time to implement and verify your understanding with path tracing and light tracing first, then try to combine them with weights.

In Kinect SDK v2.0 how do I map a pixel in the color image to a voxel in the depth image?

I know how to go the other way around. What I am looking for is, given a (x,y) coordinate in the pixel space (of the 1920x1080 image), how do I get the corresponding (if available) (x,y,z) (in meters) of the depth image. I realize that there are more pixels than voxels and it could be possible not to find any, but Microsoft's SDK has a CoordinateMapper class. This exposes the MapColorFrameToCameraSpace function. If I use that, I can get an array of points in the camera space (x,y,z) but I am unable to figure out how to extract the mapping for a specific pixel.
You probably need to use
CoordinateMapper.MapDepthFrameToColorSpace
Find the color space coordinates of all depth point.
Then, compare your pixel coordinate (x, y) with these color space coordinates. My solution is to find the closest point (might have better way), because the mapped coordinates are floats.
If you use C#, here is the code. Hope it helps!
private ushort GetDepthValueFromPixelPoint(KinectSensor kinectSensor, ushort[] depthData, float PixelX, float PixelY)
{
ushort depthValue = 0;
if (null != depthData)
{
ColorSpacePoint[] depP = new ColorSpacePoint[512 * 424];
kinectSensor.CoordinateMapper.MapDepthFrameToColorSpace(_depthData, depP);
int depthIndex = FindClosestIndex(depP, PixelX, PixelY);
if (depthIndex < 0)
Console.WriteLine("-1");
else
{
depthValue = _depthData[depthIndex];
Console.WriteLine(depthValue);
}
}
return depthValue;
}
private int FindClosestIndex(ColorSpacePoint[] depP, float PixelX, float PixelY)
{
int depthIndex = -1;
float closestPoint = float.MaxValue;
for (int j = 0; j < depP.Length; ++j)
{
float dis = DistanceOfTwoPoints(depP[j], PixelX, PixelY);
if (dis < closestPoint)
{
closestPoint = dis;
depthIndex = j;
}
}
return depthIndex;
}
private float DistanceOfTwoPoints(ColorSpacePoint colorSpacePoint, float PixelX, float PixelY)
{
float x = colorSpacePoint.X - PixelX;
float y = colorSpacePoint.Y - PixelY;
return (float)Math.Sqrt(x * x + y * y);
}

Resizing a Rectangle inside a GridPane using percentage ColumnConstraints

I have a GridPane with n columns & n rows, and a Rectangle in each cell (almost like a chess board). I'm trying to make the Rectangles expand to take up all the space available in each cell, without expanding too far. Have tried a ColumnConstraints approach, but still don't know what to bind the Rectangles' width to.
Solution: bind Rectangle width and height to a NumberBinding.
Example, makes a chess board:
GridPane board = new GridPane();
NumberBinding rectsAreaSize = Bindings.min(board.heightProperty(), board.widthProperty());
for(int i = 0; i < size; ++i)
{
for(int j = 0; j < size; ++j)
{
Rectangle rect;
if(i % 2 == 0 ^ j % 2 == 0) // ^ is the XOR operator
{
rect = new Rectangle(15.0, 15.0, Color.WHITE);
}
else
{
rect = new Rectangle(15.0, 15.0, Color.BLACK);
}
rect.widthProperty().bind(rectsAreaSize.divide(size));
rect.heightProperty().bind(rectsAreaSize.divide(size));
board.add(rect, i, j);
GridPane.setHalignment(rect, HPos.CENTER);
}
}
References:
How to create dynamically Resizable shapes in javafx?
Can a gridpane automatically resize it's objects to fit? Trying to set a max_width and max_height to a grid and have it resize content. JavaFX