# Problem with Hermite Interpolation in skinning mesh

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I'm trying to implement an skinning mesh and I use Hermite Interpolation for evaulating frame's position. When I use the normal interpolation: t1*p1 + (1-t1)*p2, it run well, but  when I change to Hermite Interpolation, the mesh seems to run in the horizontal direction as it is shown in the following video.

This is my source code and I hope you can help me put the video and the source together, and provide some suggestions about the problem.

1. Setup tangent

     for (int k = 0; k < numPositionKeys; k++)
{
// make the curve tangents looped
int k0 = k - 1;
if (k0 < 0)
k0 = numPositionKeys - 1;
int k1 = k;
int k2 = k + 1;
if (k2 >= numPositionKeys)
k2 = 0;

// calculate the tangent, which is the vector from key[k - 1] to key[k + 1]
float tangent[3];
tangent[0] = (joint->positionKeys[k2].key[0] - joint->positionKeys[k0].key[0]);
tangent[1] = (joint->positionKeys[k2].key[1] - joint->positionKeys[k0].key[1]);
tangent[2] = (joint->positionKeys[k2].key[2] - joint->positionKeys[k0].key[2]);

// weight the incoming and outgoing tangent by their time to avoid changes in speed, if the keys are not within the same interval
float dt1 = joint->positionKeys[k1].time - joint->positionKeys[k0].time;
float dt2 = joint->positionKeys[k2].time - joint->positionKeys[k1].time;
float dt = dt1 + dt2;

joint->tangents[k1].tangentIn[0] = tangent[0] * dt1 / dt;
joint->tangents[k1].tangentIn[1] = tangent[1] * dt1 / dt;
joint->tangents[k1].tangentIn[2] = tangent[2] * dt1 / dt;

joint->tangents[k1].tangentOut[0] = tangent[0] * dt2 / dt;
joint->tangents[k1].tangentOut[1] = tangent[1] * dt2 / dt;
joint->tangents[k1].tangentOut[2] = tangent[2] * dt2 / dt;
}


2. Interpolating frame's position

int i1 = -1;
int i2 = -1;

// Find two keys, where frame is in between for the position channel
for(int i = 0; i < FramePosition.size()-1; i++){

if(m_fAnimationTime >= FramePosition[i].m_fTimeStamp && m_fAnimationTime < FramePosition[i+1].m_fTimeStamp){
i1 = i;
i2 = i+1;
break;
}
}
if(i1 == -1 || i2 ==-1){
//Either take the first
if(m_fAnimationTime < m_vStates.front().m_fTimeStamp)
position = FramePosition.front();

//Or the last key
else if (m_fAnimationTime >= m_vStates.back().m_fTimeStamp)
position = FramePosition.back();
}else{

//Perform interpolation between the current frame and the next frame
//to find the current position.
//Using i1 and i2 here to get position1, tangent1, position2, tangent2
Vector3f tangentOut1 = ...[i1]
Vector3f tangentIn2 = ...[i2]
Vector3f position1 = ...[i1];
Vector3f position2 = ...[i2];

float t = (m_fAnimationTime - m_fTimeStamp1)/(m_fTimeStamp2 - m_fTimeStamp1);
float t2 = t*t;
float t3 = t2*t;

// calculate Hermite basis
float h1 =  2.0f * t3 - 3.0f * t2 + 1.0f;
float h2 = -2.0f * t3 + 3.0f * t2;
float h3 =         t3 - 2.0f * t2 + t;
float h4 =         t3 -        t2;

//And finally, interpolating...
position = h1 * position1 + h3 * tangentOut1 + h2 * position2 + h4 * tangentIn2;

}

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