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## Trouble implementing SAT collision

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### #1gracicot  Members

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Posted 16 February 2013 - 03:20 PM

Hi there,

I am currently writing a little engine from scratch but I have currently trouble implementing the SAT collision algorithm. I'm able to detect collision with stunning precision but unfortunately, I can't get the right collision response. Sometimes the object bounce, but sometime the object is shallowed inside the other one and moving inside very quickly. It's been around a week I try to figuring out what's the problem and it's get worse over time. Here's a sample of my code:

The collision detection:

Vector2 Polygon::projection(double angle) const
{
Vector2 axis = {cos(angle), sin(angle)};
Vector2 result_projection;
Vector2 current;

std::list<Vector2>::const_iterator verticle = _vertex.begin();

current = *verticle;
current.setAngle(_angle + current.getAngle());

result_projection.x = axis.dot(current + _position);
result_projection.y = result_projection.x;

for(verticle++ ; verticle != _vertex.end() ; verticle++)
{
current = *verticle;
current.setAngle(_angle + current.getAngle());
double p = axis.dot(current + _position);
if(p < result_projection.x)
{
result_projection.x = p;
}
else if(p > result_projection.y)
{
result_projection.y = p;
}
}

return result_projection;
}

Vector2 Polygon::overlap(const SAT_able& other) const
{
Vector2 overlap;
overlap.setLenght(std::numeric_limits< double >().max());
for(double angle : getAngles())
{
Vector2 projectionThis = this->projection(angle);
Vector2 projectionOther = other.projection(angle);

if(projectionThis.x < projectionOther.x && projectionThis.y > projectionOther.x && projectionThis.y < projectionOther.y)
{
if(overlap.getLenght() > projectionThis.y - projectionOther.x)
{
overlap = {projectionThis.y - projectionOther.x, 0};
overlap.setAngle(angle);
}
}
else if(projectionThis.x > projectionOther.x && projectionThis.y < projectionOther.y)
{
if(overlap.getLenght() > projectionThis.y - projectionThis.x)
{
overlap = {projectionThis.y - projectionThis.x, 0};
overlap.setAngle(angle);
}
}
else if(projectionThis.x > projectionOther.x && projectionThis.x < projectionOther.y && projectionThis.y > projectionOther.y)
{
if(overlap.getLenght() > projectionOther.y - projectionThis.x)
{
overlap = {projectionOther.y - projectionThis.x, 0};
overlap.setAngle(angle);
}
}
else if(projectionThis.x < projectionOther.x && projectionThis.y > projectionOther.y)
{
if(overlap.getLenght() > projectionOther.y - projectionOther.x)
{
overlap = {projectionOther.y - projectionOther.x};
overlap.setAngle(angle);
}
}
else
{
return Vector2(0,0);
}
}
return overlap;
}

std::vector< double > Polygon::getAngles() const
{
std::vector<double> angles;
Vector2 previous = *_vertex.rbegin();
previous.setAngle(_angle + previous.getAngle());
for(Vector2 current : _vertex)
{
current.setAngle(_angle + current.getAngle());
angles.push_back((previous - current).getAngle() - (pi / 2));
previous = current;
}
return angles;
}


The reponse code:

		Vector2 nearest = sat->distance;

point->setPulse("collision", nearest * point->getMass());

EventManager::triggerEvent("collision", new CollisionEventArgs(*sat, *point))

If you want to see more of my code check the projection on github: https://github.com/gracicot/subgine

EDIT: added more code

Edited by gracicot, 16 February 2013 - 07:14 PM.

### #2Nyssa  Members

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Posted 16 February 2013 - 08:25 PM

I haven't gone over the code in your link (sorry) but the problem you described sounds like a typical problem with simple collision response. When you detect a collision, are you pushing the objects apart before applying a collision response force? If not what will happen is in the next frame the object will try to move apart but are still overlapping/colliding and a collision response force will be created in the opposite direction. The result of that is objects that vibrate and/or explode very quickly.

Ideally you'd be doing collision detection that takes an objects velocity into account over a particular frame. So in one frame, you would detect when an impact will occur, move the object to the point of collision, apply collision response, then with any time remaining in that frame you move the object by its final velocity (which would be away from the point of impact).

The method I described above works well in simple scenes, but breaks down when many objects are colliding at once and the math becomes fairly complicated.

### #3l0k0  Members

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Posted 16 February 2013 - 10:23 PM

I'd do it like this:

void GetProjectionOnAxis(const Vector2 * pVertices, const int N, const Vector2& axisN, float &projMin, float &projMax) {
projMin = projMax = Dot(pVertices[0], axisN); // axisN assumed to be normalized
for (int i = 1; i < N; ++i) {
projMin = Min(projMin, pVertices[i]);
projMax = Max(projMax, pVertices[i]);
}
}

float GetOverlapOnAxis(const float projMinA, const float projMaxA, const float projMinB, const float projMaxB) {
float minP = Min(projMinA, projMinB);
float maxP = Max(projMaxA, projMaxB);
float overlap = maxP - minP;    // negative if no intersection
return overlap;
}

struct SATResult {
Vector2 m_normal;
float m_depth;
bool m_intersect;
};

bool TestPolygonPolygonSAT(const Vector2 * pVerts0, const int n0, const Vector2 * pVerts1, const int n1, SATResult& satOut) {
jlVector2 edge, edgePerp, edgePerpN;
float min0, max0, min1, max1;
float overlap, minOverlap = -F32_MAX;
jlVector4 minNormal;
satOut.m_intersect = false;
int j, i;
for (j = n0 - 1, i = 0; i < n0; j = i, ++i) {
// compute our orthogonal axis for each edge
edge = pVerts0[i] - pVerts0[j];
edgePerp = RightPerp(edge); // y, -x
edgePerpN = Normalize(edgePerp);
// get min/max projection on each axis
GetProjectionOnAxis(verts0, n0, edgePerpN, min0, max0);
GetProjectionOnAxis(verts1, n1, edgePerpN, min1, max1);
// if no overlap, no intersection
overlap = jlOverlapOnAxis(min0, max0, min1, max1);
// otherwise store minimum overlap value and the normal
if (overlap < 0.0f) {
return false; // have to intersect on every tested axis for SAT to return true
} else if (overlap < minOverlap) {
minOverlap = overlap;
minNormal = edgePerpN;
}
}
// now do the same thing, on pVerts1 axis
for (j = n0 - 1, i = 0; i < n0; j = i, ++i) {
// compute our orthogonal axis for each edge
edge = pVerts1[i] - pVerts1[j];
edgePerp = RightPerp(edge); // y, -x
edgePerpN = Normalize(edgePerp);
// get min/max projection on each axis
GetProjectionOnAxis(verts0, n0, edgePerpN, min0, max0);
GetProjectionOnAxis(verts1, n1, edgePerpN, min1, max1);
// if no overlap, no intersection
overlap = jlOverlapOnAxis(min0, max0, min1, max1);
// otherwise store minimum overlap value and the normal
if (overlap < 0.0f) {
return false; // have to intersect on every tested axis for SAT to return true
} else if (overlap < minOverlap) {
minOverlap = overlap;
minNormal = edgePerpN;
}
}
// if we get here they are intersecting
satOut.m_normal = minNormal;

satOut.m_depth = minOverlap;
satOut.m_intersect = true;
return true;
}



You would probably want to break the TestPolygonPolygonSAT into a helper function you call twice.  Also, I was lazy and just did this on the spot.  Pretty sure it is right though .

Edited by l0k0, 16 February 2013 - 10:24 PM.

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### #4gracicot  Members

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Posted 16 February 2013 - 11:27 PM

Ok, I tried the Nyssa advice and I got pretty random things... Sometimes it's ok and the collision is doing great, but sometimes my object just got at the opposite side of the other. It seems that my minimum overlap and angle are false... Il try the I0k0 solution and integrate it into my classes.

### #5l0k0  Members

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Posted 18 February 2013 - 03:08 PM

I would test the intersection code in isolation.  Debug draw the returned normal and depth and if they are intersecting.  If that seems accurate, it is probably an issue with the response code.  Also, post some more of the response code here.  What you have there isn't really telling us much.  Got to see the nitty gritty math to help determine what's wrong.

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A Floating Point
</shameless blog plug>

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