xiaoxumeng – Page 5 – Xiaoxu Meng

Nov14. Mesh Smoothing

Mesh smoothing:
- local averaging
- minimize local gradient energy in 3 dimensions
- Fourier transform (low pass filter) similar to local averaging idea
  - image convolution
  - F(A*B) = F(A) * F(B)
Spectral Analysis
- In general: extending eigenvalues, eigenvectors to linear operators on (continuous) functions.
- Fourior transform:
  - approximate signal as weighted sum (linear combination) of sines and cosines of different frequencies.
  - change of basis using eigenfunctions of Laplace operator (complex exponentials including sines and cosines)
  - Fourier transform function: ${\hat {f}}(\xi )=\int _{-\infty }^{\infty }f(x)\ e^{-2\pi ix\xi }\,dx,$
  - spacial domain–>frequency domain F(epsilon) complex amplitude
  - Inverse transform: $f(x)=\int _{-\infty }^{\infty }{\hat {f}}(\xi )\ e^{2\pi ix\xi }\,d\xi ,$
  - denoising: fourier transform–>filter out high frequency–>fourior inverse transform
- For mesh:
  - Intuition: Fourior transform by projecting onto eigenfunctions of Laplacian
  - mesh laplacian L is n x n matrix, n is number of vertices
    - Use PSD L (not normalized by vertex valence of voronoi area)
    - eigenvectors orthogonal
  - Project geometry onto eigenvectors.
  - reconstruction from eigenvectors associated with low frequencies
  - Chanllenge:
    - Too complex!
    - Too much computation!
Diffusion
- Laplace smoothing
  - Laplace is second derivative.
  - Smooth with Gaussian kernel.
  - backward Euler
    - solve p’ = p + mu * dt *L * p’
    - (I – mu * dt * L) p’ = p, identity matrix I
    - solve linear system for p’ in each step
    - Advantages: Allow larger time steps, no numerical stability problems.
Energy minimization
Alternatives

Falcor Material and Light Load

 bool SceneRenderer::setPerMaterialData(const CurrentWorkingData& currentData, const Material* pMaterial)
    {
        ConstantBuffer* pCB = currentData.pVars->getConstantBuffer(kPerMaterialCbName).get();
        if (pCB)
        {
            pMaterial->setIntoProgramVars(currentData.pVars, pCB, "gMaterial");
        }

        return true;
    }
    void SceneRenderer::updateVariableOffsets(const ProgramReflection* pReflector)
    {
        if (sWorldMatOffset == ConstantBuffer::kInvalidOffset)
        {
            const auto pPerMeshCbData = pReflector->getBufferDesc(kPerMeshCbName, ProgramReflection::BufferReflection::Type::Constant);

            if (pPerMeshCbData != nullptr)
            {
                assert(pPerMeshCbData->getVariableData("gWorldMat[0]")->isRowMajor == false); // We copy into CBs as column-major
                assert(pPerMeshCbData->getVariableData("gWorldInvTransposeMat[0]")->isRowMajor == false);
                assert(pPerMeshCbData->getVariableData("gWorldMat")->arraySize == pPerMeshCbData->getVariableData("gWorldInvTransposeMat")->arraySize);

                sWorldMatArraySize = pPerMeshCbData->getVariableData("gWorldMat")->arraySize;
                sWorldMatOffset = pPerMeshCbData->getVariableData("gWorldMat[0]")->location;
                sWorldInvTransposeMatOffset = pPerMeshCbData->getVariableData("gWorldInvTransposeMat[0]")->location;
                sMeshIdOffset = pPerMeshCbData->getVariableData("gMeshId")->location;
                sDrawIDOffset = pPerMeshCbData->getVariableData("gDrawId[0]")->location;
            }
        }

        if (sCameraDataOffset == ConstantBuffer::kInvalidOffset)
        {
            const auto pPerFrameCbData = pReflector->getBufferDesc(kPerFrameCbName, ProgramReflection::BufferReflection::Type::Constant);

            if (pPerFrameCbData != nullptr)
            {
                sCameraDataOffset = pPerFrameCbData->getVariableData("gCam.viewMat")->location;
                const auto& pCountOffset = pPerFrameCbData->getVariableData("gLightsCount");
                sLightCountOffset = pCountOffset ? pCountOffset->location : ConstantBuffer::kInvalidOffset;
                const auto& pLightOffset = pPerFrameCbData->getVariableData("gLights[0].worldPos");
                sLightArrayOffset = pLightOffset ? pLightOffset->location : ConstantBuffer::kInvalidOffset;
                const auto& pAmbientOffset = pPerFrameCbData->getVariableData("gAmbientLighting");
                sAmbientLightOffset = pAmbientOffset ? pAmbientOffset->location : ConstantBuffer::kInvalidOffset;
            }
        }
    }

bool SceneRenderer::setPerMaterialData(const CurrentWorkingData& currentData, const Material* pMaterial)

{

ConstantBuffer* pCB = currentData.pVars->getConstantBuffer(kPerMaterialCbName).get();

if (pCB)

{

pMaterial->setIntoProgramVars(currentData.pVars, pCB, "gMaterial");

}

return true;

}

void SceneRenderer::updateVariableOffsets(const ProgramReflection* pReflector)

{

if (sWorldMatOffset == ConstantBuffer::kInvalidOffset)

{

const auto pPerMeshCbData = pReflector->getBufferDesc(kPerMeshCbName, ProgramReflection::BufferReflection::Type::Constant);

if (pPerMeshCbData != nullptr)

{

assert(pPerMeshCbData->getVariableData("gWorldMat[0]")->isRowMajor == false); // We copy into CBs as column-major

assert(pPerMeshCbData->getVariableData("gWorldInvTransposeMat[0]")->isRowMajor == false);

assert(pPerMeshCbData->getVariableData("gWorldMat")->arraySize == pPerMeshCbData->getVariableData("gWorldInvTransposeMat")->arraySize);

sWorldMatArraySize = pPerMeshCbData->getVariableData("gWorldMat")->arraySize;

sWorldMatOffset = pPerMeshCbData->getVariableData("gWorldMat[0]")->location;

sWorldInvTransposeMatOffset = pPerMeshCbData->getVariableData("gWorldInvTransposeMat[0]")->location;

sMeshIdOffset = pPerMeshCbData->getVariableData("gMeshId")->location;

sDrawIDOffset = pPerMeshCbData->getVariableData("gDrawId[0]")->location;

}

if (sCameraDataOffset == ConstantBuffer::kInvalidOffset)

{

const auto pPerFrameCbData = pReflector->getBufferDesc(kPerFrameCbName, ProgramReflection::BufferReflection::Type::Constant);

if (pPerFrameCbData != nullptr)

{

sCameraDataOffset = pPerFrameCbData->getVariableData("gCam.viewMat")->location;

const auto& pCountOffset = pPerFrameCbData->getVariableData("gLightsCount");

sLightCountOffset = pCountOffset ? pCountOffset->location : ConstantBuffer::kInvalidOffset;

const auto& pLightOffset = pPerFrameCbData->getVariableData("gLights[0].worldPos");

sLightArrayOffset = pLightOffset ? pLightOffset->location : ConstantBuffer::kInvalidOffset;

const auto& pAmbientOffset = pPerFrameCbData->getVariableData("gAmbientLighting");

sAmbientLightOffset = pAmbientOffset ? pAmbientOffset->location : ConstantBuffer::kInvalidOffset;

}

D3D12_SIMULTANEOUS_RENDER_TARGET_COUNT = 8

740 Oct26

How to solve Linear list square min||Ax – b||^2??

https://en.wikipedia.org/wiki/Linear_least_squares_(mathematics)

How to find the transformation matrix if we don’t have the correspondence between two point clouds??

Build ruined 3D mesh:

Voronoi diagram
Delaunay triangulation
Crust in 3D

Post processing:

normal estimation and filtering

Build the curve when we are given the surface points and the normals??

triangulation Iso-surface??

Commonly Used Variables in Falcor

struct ShadingAttribs
{
float3 P; ///&lt; Shading hit position in world space
float3 E; ///&lt; Direction to the eye at shading hit
float3 N; ///&lt; Shading normal at shading hit
float3 T; ///&lt; Shading tangent at shading hit
float3 B; ///&lt; Shading bitangent at shading hit
float2 UV; ///&lt; Texture mapping coordinates

#ifdef _MS_USER_DERIVATIVES
float2 DPDX DEFAULTS(float2(0, 0));
float2 DPDY DEFAULTS(float2(0, 0)); ///&lt; User-provided 2x2 full matrix of duv/dxy derivatives of a shading point footprint in texture space
#else
float lodBias DEFAULTS(0); ///&lt; LOD bias to use when sampling textures
#endif

#ifdef _MS_USER_HALF_VECTOR_DERIVATIVES
float2 DHDX DEFAULTS(float2(0, 0));
float2 DHDY DEFAULTS(float2(0, 0)); ///&lt; User-defined half-vector derivatives
#endif
PreparedMaterialData preparedMat; ///&lt; Copy of the original material with evaluated parameters (i.e., textures are fetched etc.)
float aoFactor;
};

struct ShadingAttribs

{

float3 P; ///< Shading hit position in world space

float3 E; ///< Direction to the eye at shading hit

float3 N; ///< Shading normal at shading hit

float3 T; ///< Shading tangent at shading hit

float3 B; ///< Shading bitangent at shading hit

float2 UV; ///< Texture mapping coordinates

#ifdef _MS_USER_DERIVATIVES

float2 DPDX DEFAULTS(float2(0, 0));

float2 DPDY DEFAULTS(float2(0, 0)); ///< User-provided 2x2 full matrix of duv/dxy derivatives of a shading point footprint in texture space

#else

float lodBias DEFAULTS(0); ///< LOD bias to use when sampling textures

#endif

#ifdef _MS_USER_HALF_VECTOR_DERIVATIVES

float2 DHDX DEFAULTS(float2(0, 0));

float2 DHDY DEFAULTS(float2(0, 0)); ///< User-defined half-vector derivatives

#endif

PreparedMaterialData preparedMat; ///< Copy of the original material with evaluated parameters (i.e., textures are fetched etc.)

float aoFactor;

};

136. Single Number

Given an array of integers, every element appears twice except for one. Find that single one.

Solution:

class Solution {
public:
    int singleNumber(vector<int>& nums) {
        int A = nums[0];
        for(int i = 1; i < nums.size();i++)
        {
            A = A ^ nums[i];
        }
        return A;
    }
};

class Solution {

public:

int singleNumber(vector<int>& nums) {

int A = nums[0];

for(int i = 1; i < nums.size();i++)

{

A = A ^ nums[i];

}

return A;

}

};

The obj file of sponza model has texture coordinates beyond [0,1], it even has negative numbers! When I map it to Gbuffer, the texture2D() just went wrong. So should use vec2 newTextCoord = fract(TextCoord);

I have new keyboard!

Shang gave me a mechanical keyboard, feeling so cool with it!

09/21/2017

A 99 line global illumination: (path tracing) http://www.kevinbeason.com/smallpt/

Author: xiaoxumeng