// https://blackpawn.com/texts/pointinpoly/
bool IsSameSide(MyVector3 p1, MyVector3 p2, MyVector3 a, MyVector3 b)
{
var cp1 = MyVector3.Cross(b - a, p1 - a);
var cp2 = MyVector3.Cross(b - a, p2 - a);
return(MyVector3.Dot(cp1, cp2) >= 0);
}
List <MyVector3> ProjectTrajAccording2Profile(List <MyVector2> trajpoints)
{
List <MyVector3> output = new List <MyVector3>();
MyVector3 profilenormal = this.topCircle.Normal;
MyVector3 profilecenter = this.topCircle.Center;
MyVector3 viewvector = this.camera.target; //suppose to be (0,0,1)
//find a plane that is almost vertical to view vector and the normal line of profile is on the plane
MyVector3 temp = profilenormal.Cross(viewvector);
MyVector3 targetplanenormal = profilenormal.Cross(temp);
targetplane = new MyPlane(profilecenter, targetplanenormal);
output = this.Proj2dToPlane(targetplane, trajpoints);
return(output);
}
//calculate the x velocity resulting from the ball sliding on the floor for a time deltaTime
private MyVector3 HorizontalVelocityAfterSliding(float deltaTime)
{
if (pureRolling)
{
return(velocityPreviousFrame);
}
MyVector3 afterSlidingVel;
MyVector3 horizontal_velocityPreviousFrame =
new MyVector3(velocityPreviousFrame.getX(), 0, velocityPreviousFrame.getZ());
//calculate the variation in the angular momentum and x component of the linear momentum
float arbitraryConst1 = 5f;
MyVector3 frictionDirection = horizontal_velocityPreviousFrame.Scale(-1).UnitVector();
MyVector3 linearMomentumVariation = frictionDirection.Scale(
arbitraryConst1 * floorFriction * mass * deltaTime);
MyVector3 angularMomentumVariation = MyVector3.Cross(
new MyVector3(0, -radius, 0),
linearMomentumVariation);
afterSlidingVel = MyVector3.Add(horizontal_velocityPreviousFrame, linearMomentumVariation.Scale(1 / mass));
angularMomentumCurrentFrame = MyVector3.Add(angularMomentumCurrentFrame, angularMomentumVariation);
MyVector3 contactPointTangentVel = MyVector3.Cross(AngularVelocity(angularMomentumCurrentFrame), new MyVector3(0, -radius, 0));
if (contactPointTangentVel.Magnitude() > afterSlidingVel.Magnitude())
{
pureRolling = true;
//calculate the rolling horizintal velocity
//pure rolling law: speed = (radius) * (angular vel)
float MRsquared_over_I = (mass * radius * radius) / momentOfInertia;
afterSlidingVel =
MyVector3.Subtract(afterSlidingVel.Scale(MRsquared_over_I), contactPointTangentVel).Scale(1 / (1 + MRsquared_over_I));
angularMomentumCurrentFrame = MyVector3.Cross(afterSlidingVel, new MyVector3(0, -1, 0)).Scale(momentOfInertia / radius);
}
return(afterSlidingVel);
}
private static MyVector3 Get3PlanesInterPoint(ref MyPlane p1, ref MyPlane p2, ref MyPlane p3)
{
//P = -d1 * N2xN3 / N1.N2xN3 - d2 * N3xN1 / N2.N3xN1 - d3 * N1xN2 / N3.N1xN2
MyVector3 v =
-p1.D * MyVector3.Cross(p2.Normal, p3.Normal) / MyVector3.Dot(p1.Normal, MyVector3.Cross(p2.Normal, p3.Normal))
- p2.D * MyVector3.Cross(p3.Normal, p1.Normal) / MyVector3.Dot(p2.Normal, MyVector3.Cross(p3.Normal, p1.Normal))
- p3.D * MyVector3.Cross(p1.Normal, p2.Normal) / MyVector3.Dot(p3.Normal, MyVector3.Cross(p1.Normal, p2.Normal));
return(v);
}
/// <summary>
/// Extracts perspective camera parameters from the frustum, doesn't work with orthographic frustums.
/// </summary>
/// <returns>Perspective camera parameters from the frustum</returns>
public MyFrustumCameraParams GetCameraParams()
{
var corners = GetCorners();
var cameraParam = new MyFrustumCameraParams();
cameraParam.Position = Get3PlanesInterPoint(ref pRight, ref pTop, ref pLeft);
cameraParam.LookAtDir = pNear.Normal;
cameraParam.UpDir = MyVector3.Normalize(MyVector3.Cross(pRight.Normal, pNear.Normal));
cameraParam.FOV = (float)((Math.PI / 2.0 - Math.Acos(MyVector3.Dot(pNear.Normal, pTop.Normal))) * 2);
cameraParam.AspectRatio = (corners[6] - corners[5]).Length() / (corners[4] - corners[5]).Length();
cameraParam.ZNear = (cameraParam.Position + (pNear.Normal * pNear.D)).Length();
cameraParam.ZFar = (cameraParam.Position + (pFar.Normal * pFar.D)).Length();
return(cameraParam);
}
/// <summary>
/// Creates a new frustum relaying on perspective camera parameters
/// </summary>
/// <param name="cameraPos">The camera pos.</param>
/// <param name="lookDir">The look dir.</param>
/// <param name="upDir">Up dir.</param>
/// <param name="fov">The fov.</param>
/// <param name="znear">The znear.</param>
/// <param name="zfar">The zfar.</param>
/// <param name="aspect">The aspect.</param>
/// <returns>The bounding frustum calculated from perspective camera</returns>
public static MyBoundingFrustum FromCamera(MyVector3 cameraPos, MyVector3 lookDir, MyVector3 upDir, float fov, float znear, float zfar, float aspect)
{
//http://knol.google.com/k/view-frustum
lookDir = MyVector3.Normalize(lookDir);
upDir = MyVector3.Normalize(upDir);
MyVector3 nearCenter = cameraPos + lookDir * znear;
MyVector3 farCenter = cameraPos + lookDir * zfar;
float nearHalfHeight = (float)(znear * Math.Tan(fov / 2f));
float farHalfHeight = (float)(zfar * Math.Tan(fov / 2f));
float nearHalfWidth = nearHalfHeight * aspect;
float farHalfWidth = farHalfHeight * aspect;
MyVector3 rightDir = MyVector3.Normalize(MyVector3.Cross(upDir, lookDir));
MyVector3 Near1 = nearCenter - nearHalfHeight * upDir + nearHalfWidth * rightDir;
MyVector3 Near2 = nearCenter + nearHalfHeight * upDir + nearHalfWidth * rightDir;
MyVector3 Near3 = nearCenter + nearHalfHeight * upDir - nearHalfWidth * rightDir;
MyVector3 Near4 = nearCenter - nearHalfHeight * upDir - nearHalfWidth * rightDir;
MyVector3 Far1 = farCenter - farHalfHeight * upDir + farHalfWidth * rightDir;
MyVector3 Far2 = farCenter + farHalfHeight * upDir + farHalfWidth * rightDir;
MyVector3 Far3 = farCenter + farHalfHeight * upDir - farHalfWidth * rightDir;
MyVector3 Far4 = farCenter - farHalfHeight * upDir - farHalfWidth * rightDir;
var result = new MyBoundingFrustum();
result.pNear = new MyPlane(Near1, Near2, Near3);
result.pFar = new MyPlane(Far3, Far2, Far1);
result.pLeft = new MyPlane(Near4, Near3, Far3);
result.pRight = new MyPlane(Far1, Far2, Near2);
result.pTop = new MyPlane(Near2, Far2, Far3);
result.pBottom = new MyPlane(Far4, Far1, Near1);
result.pNear.Normalize();
result.pFar.Normalize();
result.pLeft.Normalize();
result.pRight.Normalize();
result.pTop.Normalize();
result.pBottom.Normalize();
result.pMatrix = MyMatrix.LookAtLH(cameraPos, cameraPos + lookDir * 10, upDir) * MyMatrix.PerspectiveFovLH(fov, aspect, znear, zfar);
return(result);
}
void LateUpdate()
{
//CONSTRAINTS
for (int i = jointsPositions.Length - 2; i >= 0; i--)
{
if (i > 0)
{
ToParent = new MyVector3(joints[i - 1].position.x - joints[i].position.x, joints[i - 1].position.y - joints[i].position.y, joints[i - 1].position.z - joints[i].position.z).normalized();
ToChild = new MyVector3(joints[i + 1].position.x - joints[i].position.x, joints[i + 1].position.y - joints[i].position.y, joints[i + 1].position.z - joints[i].position.z).normalized();
axis = MyVector3.Cross(ToParent, ToChild).normalized();
float angle = Mathf.Acos(MyVector3.Dot(ToParent, ToChild) / (ToParent.magnitude() * ToChild.magnitude())) * Mathf.Rad2Deg;
if (angle > maxAngle || angle < ((i == 1) ? minAngle * 4 : minAngle))
{
angle = Mathf.Clamp(angle, ((i == 1) ? minAngle * 4 : minAngle), maxAngle);
joints[i].rotation = joints[i - 1].rotation;
joints[i].Rotate(new Vector3(axis.x, axis.y, axis.z), 180 + angle, Space.World);
}
}
else if (i == 0)
{
ToParent = new MyVector3(0, -1, 0);
ToChild = new MyVector3(joints[i + 1].position.x - joints[i].position.x, joints[i + 1].position.y - joints[i].position.y, joints[i + 1].position.z - joints[i].position.z).normalized();
axis = MyVector3.Cross(ToParent, ToChild).normalized();
float angle = Mathf.Acos(MyVector3.Dot(ToParent, ToChild) / (ToParent.magnitude() * ToChild.magnitude())) * Mathf.Rad2Deg;
if (angle > maxAngle + maxAngle / 4 || angle < maxAngle - maxAngle / 4)
{
angle = Mathf.Clamp(angle, maxAngle - maxAngle / 4, maxAngle + maxAngle / 4);
joints[i].rotation = Quaternion.identity;
joints[i].Rotate(new Vector3(axis.x, axis.y, axis.z), 240 + angle, Space.World);
}
}
}
}
void Update()
{
// Copy the joints positions to work with
//TODO
copy[0] = new MyVector3(joints[0].position);
//copy[0] = joints[0].position;
for (int i = 0; i < joints.Length - 1; i++)
{
copy[i + 1] = new MyVector3(joints[i + 1].position);
distances[i] = (copy[i + 1] - copy[i]).Module();
//copy[i + 1] = joints[i + 1].position;
//distances[i] = (copy[i + 1] - copy[i]).magnitude;
}
// CALCULATE ALSO THE DISTANCE BETWEEN JOINTS
//done = TODO
done = (copy[copy.Length - 1] - new MyVector3(target.position)).Module() < tresholdCondition;
//done = (copy[copy.Length - 1] - target.position).magnitude < tresholdCondition;
if (!done)
{
float targetRootDist = (copy[0] - new MyVector3(target.position)).Module();
//float targetRootDist = Vector3.Distance(copy[0], target.position);
// Update joint positions
if (targetRootDist > distances.Sum())
{
// The target is unreachable
for (int i = 0; i < copy.Length - 1; i++)
{
float r = (new MyVector3(target.position) - copy[i]).Module();
//float r = (target.position - copy[i]).magnitude;
float lambda = distances[i] / r;
copy[i + 1] = (1 - lambda) * copy[i] + (lambda * new MyVector3(target.position));
//copy[i + 1] = (1 - lambda) * copy[i] + (lambda * target.position);
}
}
else
{
MyVector3 b = copy[0];
//Vector3 b = copy[0];
// The target is reachable
//while (TODO)
float difference = (copy[copy.Length - 1] - new MyVector3(target.position)).Module();
//float difference = (copy[copy.Length - 1] - target.position).magnitude;
while (difference > tresholdCondition) // treshold = tolerance
{
// numIterations++;
// STAGE 1: FORWARD REACHING
//TODO
copy[copy.Length - 1] = new MyVector3(target.position);
//copy[copy.Length - 1] = target.position;
for (int i = copy.Length - 2; i > 0; i--)
{
float r = (copy[i + 1] - copy[i]).Module();
//float r = (copy[i + 1] - copy[i]).magnitude;
float lambda = distances[i] / r;
copy[i] = (1 - lambda) * copy[i + 1] + lambda * copy[i];
}
// STAGE 2: BACKWARD REACHING
//TODO
copy[0] = b;
for (int i = 0; i < copy.Length - 1; i++)
{
float r = (copy[i + 1] - copy[i]).Module();
//float r = (copy[i + 1] - copy[i]).magnitude;
float lambda = distances[i] / r;
copy[i + 1] = (1 - lambda) * copy[i] + lambda * copy[i + 1];
}
difference = (copy[copy.Length - 1] - new MyVector3(target.position)).Module();
//difference = (copy[copy.Length - 1] - target.position).magnitude;
}
}
// Update original joint rotations
for (int i = 0; i <= joints.Length - 2; i++)
{
// float originalAngle = joints[i].rotation.w;
MyQuat parentRotation = new MyQuat(joints[i + 1].rotation);
MyQuat childRotation = new MyQuat(joints[i].rotation);
//TODO
// Rotation
MyVector3 vectorA = new MyVector3(joints[i + 1].position) - new MyVector3(joints[i].position);
MyVector3 vectorB = copy[i + 1] - copy[i];
//Vector3 vectorA = joints[i + 1].position - joints[i].position;
//Vector3 vectorB = copy[i + 1] - copy[i];
// float angle = Mathf.Acos(Vector3.Dot(vectorA.normalized, vectorB.normalized)) * Mathf.Rad2Deg;
float cosA = (MyVector3.Dot(vectorA.Normalize(), vectorB.Normalize()));
float sinA = MyVector3.Cross(vectorA.Normalize(), vectorB.Normalize()).Module();
//float cosA = (Vector3.Dot(vectorA.normalized, vectorB.normalized));
//float sinA = Vector3.Cross(vectorA.normalized, vectorB.normalized).magnitude;
// Atan = Cos | Atan2 = denominador y...
float angle = Mathf.Atan2(sinA, cosA) * Mathf.Rad2Deg;
MyVector3 axis = MyVector3.Cross(vectorA, vectorB).Normalize();
//Vector3 axis = Vector3.Cross(vectorA, vectorB).normalized;
// joints[i].rotation = Quaternion.AngleAxis(angle, axis) * joints[i].rotation;
joints[i].rotation = MyQuat.Multiply(MyQuat.Axis2Quad(angle, axis), childRotation).ToUnityQuat();
//joints[i].rotation = MyQuat.Multiply(MyQuat.Axis2Quad(angle, axis), childRotation).ToUnityQuat();
childRotation = new MyQuat(joints[i].rotation);
float angleTest = MyQuat.Angle(parentRotation, childRotation);
if (Mathf.Abs(angleTest) > maxAngleRotation)
{
joints[i + 1].rotation = joints[i].rotation;
}
joints[i + 1].position = new Vector3(copy[i + 1].x, copy[i + 1].y, copy[i + 1].z);
//joints[i + 1].position = copy[i + 1];
}
}
}
void Update()
{
// Copy the joints positions to work with
for (int i = 0; i < joints.Length; i++)
{
copy[i] = new MyVector3(joints[i].position.x, joints[i].position.y, joints[i].position.z); //Copy the joints
if (i < joints.Length - 1)
{
distances[i] = MyVector3.Distance(joints[i + 1].position, joints[i].position); //Calculate the distances
}
}
done = (copy[copy.Length - 1] - new MyVector3(target.position.x, target.position.y, target.position.z)).magnitude < treshold_condition;
if (!done)
{
float targetRootDist = MyVector3.Distance(copy[0], new MyVector3(target.position.x, target.position.y, target.position.z));
// Update joint positions
if (targetRootDist > distances.Sum())
{
// The target is unreachable
for (int i = 0; i < copy.Length - 1; i++)
{
float r = (new MyVector3(target.position.x, target.position.y, target.position.z) - copy[i]).magnitude;
float lambda = distances[i] / r;
copy[i + 1] = copy[i] * (1 - lambda) + new MyVector3(target.position.x, target.position.y, target.position.z) * lambda;
}
}
else
{
MyVector3 b = copy[0];
float difA = (copy[copy.Length - 1] - new MyVector3(target.position.x, target.position.y, target.position.z)).magnitude;
// The target is reachable
while (difA > treshold_condition)
{
// STAGE 1: FORWARD REACHING
copy[copy.Length - 1] = new MyVector3(target.position.x, target.position.y, target.position.z);
for (int i = copy.Length - 2; i > 0; i--)
{
float r = (copy[i + 1] - copy[i]).magnitude;
float lambda = distances[i] / r;
copy[i] = copy[i + 1] * (1 - lambda) + copy[i] * lambda;
}
// STAGE 2: BACKWARD REACHING
copy[0] = b;
for (int i = 0; i < copy.Length - 1; i++)
{
float r = (copy[i + 1] - copy[i]).magnitude;
float lambda = distances[i] / r;
copy[i + 1] = copy[i] * (1 - lambda) + copy[i + 1] * lambda;
}
difA = (copy[copy.Length - 1] - new MyVector3(target.position.x, target.position.y, target.position.z)).magnitude;
}
}
// Update original joint rotations
for (int i = 0; i <= joints.Length - 2; i++)
{
MyQuaternion parentQuat = new MyQuaternion(joints[i + 1].rotation);
MyQuaternion myQuat = new MyQuaternion(joints[i].rotation);
MyVector3 A = new MyVector3(joints[i + 1].position - joints[i].position);
MyVector3 B = copy[i + 1] - copy[i];
float cosa = MyVector3.Dot(MyVector3.Normalize(A), MyVector3.Normalize(B));
float sina = MyVector3.Cross(MyVector3.Normalize(A), MyVector3.Normalize(B)).magnitude;
float alpha = Mathf.Atan2(sina, cosa) * Mathf.Rad2Deg;
MyVector3 myAxis = MyVector3.Normalize(MyVector3.Cross(A, B));
//Vector3 axis = new Vector3(myAxis.x, myAxis.y, myAxis.z);
myQuat = MyQuaternion.AngleAxis(alpha, ref myAxis);
Quaternion quat = new Quaternion(myQuat.x, myQuat.y, myQuat.z, myQuat.w);
joints[i].rotation = quat * joints[i].rotation;
//joints[i].rotation = Quaternion.AngleAxis(alpha, axis) * joints[i].rotation;
myQuat = new MyQuaternion(joints[i].rotation);
float localAngle = MyQuaternion.Angle(parentQuat, myQuat);
if (Mathf.Abs(localAngle) > maxRotation)
{
joints[i + 1].rotation = joints[i].rotation;
}
joints[i + 1].position = new Vector3(copy[i + 1].x, copy[i + 1].y, copy[i + 1].z);
}
}
}
private void RayTracein3DPlane(List <MyVector3> points, MyVector3 curp, MyVector3 curdire, MyVector3 sectionPlaneNormal, out int norInsec, out int notNorInsec)
{
// Param
double insecPs_Dist_theshold = 0.01;
double insecP_DistBetweenRay_theshold = 20;
MyVector3 cutNormal = sectionPlaneNormal.Cross(curdire).Normalize();
ray = new Line3(curp, cutNormal);
norInsec = -1; // Normal side
notNorInsec = -1; // Not Normal side
double dist_left = double.MaxValue;
double dist_right = double.MaxValue;
for (int i = 0; i < points.Count; i++)
{
double dist_temp = ray.DistanceToLine(points[i]);
if ((points[i] - curp).Dot(cutNormal) > 0)
{
// Normal side
if (dist_left > dist_temp)
{
dist_left = dist_temp;
norInsec = i;
}
}
else
{
// Not Normal side
if (dist_right > dist_temp)
{
dist_right = dist_temp;
notNorInsec = i;
}
}
}
if (norInsec == -1)
{
norInsec = notNorInsec;
System.Console.WriteLine("Warining: norInsec == -1");
return;
}
else if (notNorInsec == -1)
{
notNorInsec = norInsec;
System.Console.WriteLine("Warining: notNorInsec == -1");
return;
}
else if (norInsec == -1 && notNorInsec == -1)
{
System.Console.WriteLine("Error: Ray Tracein3DPlane, no intersection points");
return;
}
if (MyVector3.Distance(points[norInsec], points[notNorInsec]) < insecPs_Dist_theshold)
{
// this two intersection is too close, so let them become same one.s
System.Console.WriteLine("Warining: two intersection is too close");
norInsec = notNorInsec;
return;
}
if (ray.DistanceToLine(points[norInsec]) > insecP_DistBetweenRay_theshold ||
ray.DistanceToLine(points[notNorInsec]) > insecP_DistBetweenRay_theshold)
{
System.Console.WriteLine("Warining: two intersection is too far");
// this two intersection is too far, so let them become same one.s
norInsec = notNorInsec;
return;
}
}
public void CylinderSnapping()
{
// Get Boundary2
if (boundaryPoints_2d == null)
{
boundaryPoints_2d = GetBoundaryPoints(mark);
}
List <MyVector2> boundary2 = ExtractOutline(edgeImage, boundaryPoints_2d);
// Project 2D edge points
//topCircle = new MyCircle(topCircle.Center, topCircle.Radius, -topCircle.Normal);
MyVector3 normal = topCircle.Normal.Cross(this.camera.target).Cross(topCircle.Normal);
MyPlane sectionPlane = new MyPlane(topCircle.Center, normal);
boundary3 = Proj2dToPlane(sectionPlane, boundary2);
topCircle = CiriFixTopCircle(topCircle, boundary3);
// UpdateCircleNormal
// foreach (var pbondary3 in pbondary3)
// {
// }
// if (topCircle.Center)
//{
//}
// Algorithm Init Params
double offset = topCircle.Radius / 50;
cur_p = topCircle.Center - offset * topCircle.Normal;
cur_dire = 1.0 * topCircle.Normal;
MyVector3 cur_dire_new = new MyVector3(cur_dire);
MyVector3 cur_p_new = new MyVector3(-1 * cur_p);
Insection1 = new MyVector3(1, 1, 1);
Insection2 = new MyVector3(0, 0, 0);
int norInsec = -1;
int notNorInsec = -1;
MyVector3 tangential1 = new MyVector3(1, 1, 1);
MyVector3 tangential2 = new MyVector3(1, 1, 1);
List <MyCircle> CircleLists = new List <MyCircle>();
CircleLists.Add(topCircle); // Fix first circle
int iter = 0;
double r = double.MaxValue;
System.Console.WriteLine(Insection1.Dot(tangential2));
System.Console.WriteLine(Math.Cos(2.0 / 3.0 * Math.PI));
int MaxInter = 1000;
GeneratedCenters = new List <MyVector3>();
List <double> radius = new List <double>();
List <double> weights = new List <double>();
List <MyVector3> dires = new List <MyVector3>();
while (--MaxInter > 0) //
{
if (Insection1 == Insection2) // 交点一直保持相同
{
System.Console.WriteLine("Warning: Insection is same!"); // 半径过小
break;
}
if (cur_dire.Dot(cur_dire_new) < 0) // 移动方向反向
{
System.Console.WriteLine("Warning: Move Direction！");
break;
}
if (cur_p + offset * cur_dire == cur_p_new) // 中心点没有移动
{
System.Console.WriteLine("Warning: Center not move!");
break;
}
RayTracein3DPlane(boundary3,
cur_p_new,
cur_dire_new.Cross(sectionPlane.Normal()),
sectionPlane.Normal(),
out norInsec,
out notNorInsec);
System.Console.WriteLine("{0} , {1}",
MyVector3.Distance(boundary3[norInsec], cur_p_new),
MyVector3.Distance(boundary3[notNorInsec], cur_p_new));
test1 = new Line3(boundary3[norInsec], cur_p_new - boundary3[norInsec]);
test2 = new Line3(boundary3[notNorInsec], cur_p_new - boundary3[notNorInsec]);
if (MyVector3.Distance(boundary3[norInsec], cur_p_new) < topCircle.Radius / 20 || // close to bottom
MyVector3.Distance(boundary3[notNorInsec], cur_p_new) < topCircle.Radius / 20)
{
System.Console.WriteLine("Warning: Close to bottom!");
break;
}
if (tangential1.Dot(tangential2) < Math.Cos(2.0 / 3.0 * Math.PI)) //切线相向
{
System.Console.WriteLine("Warning: tangential get oppsite direction!");
break;
}
if (r < 0.0001)
{
System.Console.WriteLine("Warning: Radius is too small!"); // 半径过小
break;
}
//if (MyVector3.Distance(cur_p, cur_p_new) )
//{
// System.Console.WriteLine("Warning: Radius is too small!"); // 半径过小
// break;
//}
if (iter != 0)
{
//offset = 1 / MyVector3.Distance(cur_p, cur_p_new) * 0.000001 + 0.5 * offset;
offset = topCircle.Radius / 20;
//System.Console.WriteLine("{0}", offset);
cur_dire = cur_dire_new;
cur_p = cur_p_new + offset * cur_dire;
CircleLists.Add(new MyCircle(cur_p, r, cur_dire));
// Get Data for Fit
double weight = Math.Abs(cur_dire_new.Dot(cur_dire));
GeneratedCenters.Add(cur_p_new);
weights.Add(weight);
radius.Add(r);
dires.Add(cur_dire);
}
// Step1: Get IntersectionPoitn
RayTracein3DPlane(boundary3, cur_p, cur_dire, sectionPlane.Normal(), out norInsec, out notNorInsec);
// Step2 : Get Two Local Tangential
Insection1 = boundary3[norInsec];
Insection2 = boundary3[notNorInsec];
tangential1 = GetLocalTangential(norInsec, boundary3, cur_dire);
tangential2 = GetLocalTangential(notNorInsec, boundary3, cur_dire);
// Visualization
setdirecLine = new Line3(cur_p, cur_dire);
setLine1 = new Line3(Insection1, tangential1);
setLine2 = new Line3(Insection2, tangential2);
// Step3 : Get New Cur Direction and Cur Point
cur_dire_new = (tangential1 + tangential2) / 2;
RayTracein3DPlane(boundary3, cur_p, cur_dire_new, sectionPlane.Normal(), out norInsec, out notNorInsec);
cur_p_new = (boundary3[norInsec] + boundary3[notNorInsec]) / 2;
r = 0.5 * MyVector3.Distance(boundary3[norInsec], boundary3[notNorInsec]);
iter++;
this.view.Refresh();
}
// Fit centers and radius;
GeneratedCenters = FittingCentersCurve(GeneratedCenters, weights);
int inter = 1;
while (inter-- > 0)
{
radius = FittRadius(radius);
}
// ReBuild Object
CircleLists.Clear();
CircleLists.Add(topCircle); // Fix first circle
for (int i = 0; i < GeneratedCenters.Count; i++)
{
CircleLists.Add(new MyCircle(GeneratedCenters[i], radius[i], dires[i]));
}
CurveCyliner = new SweepMesh(CircleLists);
}
void Update()
{
if (target.position.y > 1.25f)
{
for (int i = 0; i < joints.Length; i++)
{
jointsPositions[i] = new MyVector3(joints[i].position.x, joints[i].position.y, joints[i].position.z);
}
targetPosition = new MyVector3(target.position.x, target.position.y, target.position.z);
// Copy the joints positions to work with
// and calculate all the distances
for (int i = 0; i < copy.Length; i++)
{
copy[i] = jointsPositions[i];
if (i < distances.Length)
{
distances[i] = (jointsPositions[i + 1] - jointsPositions[i]).magnitude();
}
}
done = (targetPosition - jointsPositions[jointsPositions.Length - 1]).magnitude() < threshold_distance;
if (!done)
{
float targetRootDist = MyVector3.Distance(copy[0], targetPosition);
// Update joint positions
if (targetRootDist > distances.Sum())
{
// The target is unreachable
for (int i = 0; i < copy.Length - 1; i++)
{
float dist = (targetPosition - copy[i]).magnitude();
float lam = distances[i] / dist;
copy[i + 1] = (1 - lam) * copy[i] + lam * targetPosition;
}
}
else
{
// The target is reachable
iter = 0;
while (!done /*|| iter < maxIter*/)
{
// STAGE 1: FORWARD REACHING
copy[copy.Length - 1] = targetPosition;
for (int i = copy.Length - 1; i > 0; i--)
{
MyVector3 temp = (copy[i - 1] - copy[i]).normalized();
temp = temp * distances[i - 1];
copy[i - 1] = temp + copy[i];
}
// STAGE 2: BACKWARD REACHING
copy[0] = jointsPositions[0];
for (int i = 0; i < copy.Length - 2; i++)
{
MyVector3 temp = (copy[i + 1] - copy[i]).normalized();
temp = temp * distances[i];
copy[i + 1] = temp + copy[i];
}
done = (targetPosition - copy[copy.Length - 1]).magnitude() < threshold_distance;
iter++;
}
}
// Update original joint rotations
for (int i = 0; i <= joints.Length - 2; i++)
{
MyVector3 a = jointsPositions[i + 1] - jointsPositions[i];
MyVector3 b = copy[i + 1] - copy[i];
MyVector3 axis = MyVector3.Cross(a, b).normalized();
float cosa = MyVector3.Dot(a, b) / (a.magnitude() * b.magnitude());
float sina = MyVector3.Cross(a.normalized(), b.normalized()).magnitude();
float angle = Mathf.Atan2(sina, cosa);
MyQuaternion q = new MyQuaternion(Mathf.Cos(angle / 2), axis.x * Mathf.Sin(angle / 2), axis.y * Mathf.Sin(angle / 2), axis.z * Mathf.Sin(angle / 2));
MyQuaternion actualRot = new MyQuaternion(joints[i].rotation.w, joints[i].rotation.x, joints[i].rotation.y, joints[i].rotation.z);
MyQuaternion newRot = MyQuaternion.multiply(q, actualRot);
jointsPositions[i] = copy[i];
joints[i].position = new Vector3(jointsPositions[i].x, jointsPositions[i].y, jointsPositions[i].z);
joints[i].rotation = new Quaternion(newRot.x, newRot.y, newRot.z, newRot.w);
for (int j = i; j < joints.Length; j++) //Actualizar posiciones de los hijos despues de rotar
{
jointsPositions[j] = new MyVector3(joints[j].position.x, joints[j].position.y, joints[j].position.z);
}
}
}
}
}
private void FixedUpdate()
{
//simulation start upon press of the spacebar
if (Input.GetKeyDown(KeyCode.Space) == true)
{
startSimulation = true;
}
if (!startSimulation)
{
return;
}
if (fullStop)
{
return; //simulation ended
}
float t = Time.fixedDeltaTime;
if (stopBouncing)
{
if (pureRolling)
{//case 1: the ball is rolling on the floor without sliding
float dumping = 1 -
(5 - 4 / (1 + mass)) *
(floorFriction / (4 * floorFriction + 6)) *
(1 + 49 / (1 + 10 * Mathf.Abs(velocityPreviousFrame.Magnitude()))) *
t; //arbitrary dumping factor. No real physical meaning.
velocityCurrentFrame = velocityPreviousFrame.Scale(dumping);
if (velocityCurrentFrame.Magnitude() < 0.01f)
{//the velocity is low enough to be neglectable
velocityCurrentFrame = MyVector3.Zero();
fullStop = true;
}
//calculate the avarage velocity between two consecutive frames and use it to calculate the new position
MyVector3 avgVelocity = MyVector3.Lerp(velocityPreviousFrame, velocityCurrentFrame, 0.5f);
MyVector3 displacement = avgVelocity.Scale(t);
position = MyVector3.Add(position, displacement);
MoveGameObject();
angularMomentumCurrentFrame = MyVector3.Cross(velocityCurrentFrame, new MyVector3(0, -1, 0)).Scale(momentOfInertia / radius);
RotateGameObject(t);
velocityPreviousFrame = velocityCurrentFrame;
angularMomentumPreviousFrame = angularMomentumCurrentFrame;
}
else
{//case 2: the ball is rolling on the floor with sliding
velocityCurrentFrame = HorizontalVelocityAfterSliding(t);
//calculate the avarage velocity between two consecutive frames and use it to calculate the new position
MyVector3 avgVelocity = MyVector3.Lerp(velocityPreviousFrame, velocityCurrentFrame, 0.5f);
MyVector3 displacement = avgVelocity.Scale(t);
position = MyVector3.Add(position, displacement);
MoveGameObject();
//angularMomentumCurrentFrame set in the X_VelocityAfterSliding() function
RotateGameObject(t);
velocityPreviousFrame = velocityCurrentFrame;
angularMomentumPreviousFrame = angularMomentumCurrentFrame;
}
}
else
{//the ball is still bouncing
MyVector3 deltaVel = gravity.Scale(t);
velocityCurrentFrame = MyVector3.Add(velocityPreviousFrame, deltaVel);
//calculate the avarage velocity between two consecutive frames and use it to calculate the new position
MyVector3 avgVelocity = MyVector3.Lerp(velocityPreviousFrame, velocityCurrentFrame, 0.5f);
MyVector3 displacement = avgVelocity.Scale(t);
MyVector3 newPosition = MyVector3.Add(position, displacement);
float distanceFromGround = newPosition.DistanceFromPlane(ground) - radius;
if (distanceFromGround < 0)
{ //case 3: the ball is bouncing and has partially fallen balow the plane of the ground
float impactVel_y = Y_ImpactVelocity();
float velocityCurrentFrame_y = impactVel_y * restitution; //upwards speed after bounce
if (velocityCurrentFrame_y < tresholdStopBouncing)
{ //the speed after the bounce is small enough to be ignored
stopBouncing = true;
velocityCurrentFrame_y = 0;
}
MyVector3 horzVelocityCurrentFrame = HorizontalVelocityAfterSliding(t + 0.001f * impactVel_y + 8 * t * (1 - 1 / Mathf.Sqrt(1 + mass)));
//position ball on top of the ground
position = MyVector3.Add(newPosition, ground.Normal().Scale(-distanceFromGround));
MoveGameObject();
//angularMomentumCurrentFrame set in the X_VelocityAfterSliding() function
RotateGameObject(t);
angularMomentumPreviousFrame = angularMomentumCurrentFrame;
velocityPreviousFrame = new MyVector3(horzVelocityCurrentFrame.getX(), velocityCurrentFrame_y, horzVelocityCurrentFrame.getZ());
}
else
{//case 4: the ball is bouncing and is in mid-air
velocityPreviousFrame = velocityCurrentFrame;
position = newPosition;
MoveGameObject();
RotateGameObject(t);
}
}
}
public static MyVector3 Cross(MyVector2 a, MyVector2 b)
{
return(MyVector3.Cross(a, b));
}
// Running the solver - all the joints are iterated through once every frame
void Update()
{
// if the target hasn't been reached
if (!done)
{
// if the Max number of tries hasn't been reached
if (tries <= Mtries)
{
// starting from the second last joint (the last being the end effector)
// going back up to the root
for (int i = joints.Length - 2; i >= 0; i--)
{
// The vector from the ith joint to the end effector
MyVector3 r1 = new MyVector3(joints[joints.Length - 1].position - joints[i].position);
// The vector from the ith joint to the target
MyVector3 r2 = tpos - new MyVector3(joints[i].position);
// to avoid dividing by tiny numbers
if (r1.magnitude * r2.magnitude <= 0.001f)
{
cos[i] = 1.0f;
sin[i] = 0.0f;
}
else
{
// find the components using dot and cross product
cos[i] = MyVector3.Dot(r1, r2) / (r1.magnitude * r2.magnitude);
sin[i] = MyVector3.Cross(r1, r2).magnitude / (r1.magnitude * r2.magnitude);
}
// The axis of rotation
MyVector3 axis = MyVector3.Cross(r1, r2);
// find the angle between r1 and r2 (and clamp values if needed avoid errors)
theta[i] = Mathf.Acos(cos[i]);
//Optional. correct angles if needed, depending on angles invert angle if sin component is negative
if (sin[i] < 0)
{
theta[i] *= -1;
}
// obtain an angle value between -pi and pi, and then convert to degrees
theta[i] *= Mathf.Rad2Deg;
// rotate the ith joint along the axis by theta degrees in the world space.
MyQuaternion quat = MyQuaternion.AngleAxis(theta[i], ref axis);
Quaternion fQuat = new Quaternion(quat.x, quat.y, quat.z, quat.w);
joints[i].rotation = fQuat * joints[i].rotation;
}
// increment tries
tries++;
}
}
// find the difference in the positions of the end effector and the target
float dif = (tpos - new MyVector3(joints[joints.Length - 1].position)).magnitude;
// if target is within reach (within epsilon) then the process is done
if (dif < epsilon)
{
done = true;
}
// if it isn't, then the process should be repeated
else
{
done = false;
}
// the target has moved, reset tries to 0 and change tpos
if (new MyVector3(targ.position) != tpos)
{
tries = 0;
tpos = new MyVector3(targ.position);
}
}
