Math Question

This is a discussion on Math Question within the Game Programming forums, part of the General Programming Boards category; First, I want to say that math is not exactly my strong point. In fact, I am terrible at anything ...

  1. #1
    Darkness Prevails Dark_Phoenix's Avatar
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    Math Question

    First, I want to say that math is not exactly my strong point. In fact, I am terrible at anything above basic algebra.

    I am trying to create a collision detection routine that will compute the angle of deflection. i.e. a ball hitting a wall. I can do this simply by reversing the sign of the direction vector, but this only works for a flat surface. I will have some curved / angled walls that I will need to calculate for. I know I need to start off by finding the angle between the ball's direction vector and the plane normal but I am not exactly sure how to go about this.

    If anyone can explain or point me to a good tutorial??
    Using Code::Blocks and Windows XP

    In every hero, there COULD be a villain!

  2. #2
    Crazy Fool Perspective's Avatar
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    You calculate the normal by computing the first derivative at the point of intersection. Then you can just do an incident angle reflection against the hyper plane orthogonal to that normal.

    In practive this computation would be pretty expensive for a game, I'm sure there are some type of approximations, though I don't know of anything specifically.

  3. #3
    Darkness Prevails Dark_Phoenix's Avatar
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    Well, I came up with a function to calculate the reflection angle based on the objects velocity vector and the normal of the intersected face of the mesh. I pluged it into a small console app to test it and the numbers seem to work.
    Code:
    int main() {
        D3DXVECTOR3 OldVelocity(4.0f, -2.0f, 1.0f), // Object velocity vector before collision
                    PlaneNormal(0.0f,  1.0f, 0.0f), // Direction plane is facing
                    NewVelocity;                    // Object velocity vector after collision
        
        std::cout<<OldVelocity.x <<"," <<OldVelocity.y <<"," <<OldVelocity.z <<"\n";
        
        float dot = (D3DXVec3Dot(&-OldVelocity, &PlaneNormal) );    
        NewVelocity = (2 * dot) * PlaneNormal + OldVelocity;
        
        std::cout<<NewVelocity.x <<"," <<NewVelocity.y <<"," <<NewVelocity.z <<"\n";
        
        std::cin.get();
        return 0;
    }
    Whatever numbers i assign to OldVelocity get mirrored over whatever numbers I assign to PlaneNormal, which is exactly what I need.

    My only problem now is how to get the normal of the face that was intersected. I know I can use D3DXIntersect to get the index value of the face, but how do I get the face normal from this?
    Using Code::Blocks and Windows XP

    In every hero, there COULD be a villain!

  4. #4
    Darkness Prevails Dark_Phoenix's Avatar
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    Here's what I have managed to come up with
    Code:
    bool CCollisionManager::FindNewVelocity(LPDIRECT3DDEVICE9 pDevice,
                                            CMeshInstance* pMesh,
                                            D3DXVECTOR3* pObjectPosition,
                                            D3DXVECTOR3* pOldVelocity, 
                                            D3DXVECTOR3* pNewVelocity) {
        BOOL Hit = FALSE;
        float u, v, dist;
        DWORD FaceIndex;
        D3DXVECTOR3 ObjectDirection,
                    PrevObjectDirection,
                    Velocity = -(*pOldVelocity);
    
        D3DXVECTOR3 PrevObjectPosition = *pObjectPosition - *pOldVelocity;
        D3DXVec3Normalize(&ObjectDirection, &PrevObjectDirection);
        
        // Get the normal of the intersected mesh face
        // First, Get the vertex and index buffers for the mesh
        LPDIRECT3DVERTEXBUFFER9 pVB;
        LPDIRECT3DINDEXBUFFER9  pIB;
    
        pMesh->GetMesh()->GetVertexBuffer(&pVB);
        pMesh->GetMesh()->GetIndexBuffer(&pIB);
    
        WORD                                *pIndices               = NULL;
        WORD                                *pIntersectedFaceIndex  = NULL;
        cstmVertex::PositionNormalTextured  *pVertices              = NULL;
        cstmVertex::PositionNormalTextured  *pIntersectedFaceVertex = NULL;
    
        pIB->Lock(0, 0, (void**)&pIndices, 0);
        pVB->Lock(0, 0, (void**)&pVertices, 0);
    
        // Now find which mesh face was intersected
        pDevice->SetTransform(D3DTS_WORLD, pMesh->GetTransform() ); 
        D3DXIntersect(pMesh->GetMesh(),
                      &PrevObjectPosition,
                      &ObjectDirection,
                      &Hit,
                      &FaceIndex,
                      &u, &v, &dist,
                      NULL, NULL);
    
        pIntersectedFaceIndex  = &pIndices[3 * FaceIndex];
        pIntersectedFaceVertex = &pVertices[*pIntersectedFaceIndex];
        
        pVB->Unlock();
        pIB->Unlock();
        
        // Get the normal for the face 
        D3DXVECTOR3 PlaneNormal(pIntersectedFaceVertex->Nx,
                                pIntersectedFaceVertex->Ny,
                                pIntersectedFaceVertex->Nz);
        
        // compute new velocity vector
        if (Hit == TRUE) {
            float dot = (D3DXVec3Dot(&Velocity, &PlaneNormal) );
            *pNewVelocity = (2 * dot) * PlaneNormal + *pOldVelocity;
        } else {
            *pNewVelocity = *pOldVelocity;
        }
        
        return Hit;
    }
    Everything seems to work fine except for two issues :
    • If there is a collision on any axis other than X I get a seg fault

    • no mater which face was intersected, I allways get a face normal of (0.0, -1.0, 0.0)

    I adapted this from the DX9 SDK sample 'Pick.cpp'

    Anyone have any ideas as to what is going on? I've tried everything I can think of and am still at a loss.

    Am I even on the right track here? Or is there a better way of getting the face normal?
    Last edited by Dark_Phoenix; 01-21-2007 at 08:44 AM.
    Using Code::Blocks and Windows XP

    In every hero, there COULD be a villain!

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