/// <summary>
/// return the closest point on the disc from K, if the GravityInfo permit it
/// </summary>
/// <param name="k"></param>
/// <param name="canApplyGravity"></param>
/// <param name="gravityDisc"></param>
/// <returns></returns>
public bool GetClosestPointOnDiscIfWeCan(Vector3 k, GravityOverrideDisc gravityDisc, out Vector3 closestPoint)
{
closestPoint = Vector3.zero;
if (!gravityDisc.CanApplyGravity || (!AllowBottom && !_plane.IsAbove(k)))
{
return(false);
}
//project point to a plane
Vector3 kProjected = ExtPlane.ProjectPointInPlane(_plane, k);
//if dist² < radius², this projected point is inside the circle
float distSquared = (kProjected - _plane.Point).sqrMagnitude;
bool isInsideShape = distSquared < _radiusSquared;
if (isInsideShape)
{
if (!gravityDisc.Face)
{
return(false);
}
closestPoint = kProjected;
return(true);
}
if (!gravityDisc.Borders)
{
return(false);
}
//return the closest point on the circle (extremity of the disc)
closestPoint = _plane.Point + (kProjected - _plane.Point).FastNormalized() * _radius;
return(true);
}
/// <summary>
/// Get the intersection between a line and a plane.
// If the line and plane are not parallel, the function outputs true, otherwise false.
/// </summary>
/// <param name="intersection"></param>
/// <param name="ray"></param>
/// <param name="plane"></param>
/// <returns></returns>
public static bool LinePlaneIntersection(out Vector3 intersection, Ray ray, ExtPlane plane)
{
float length;
float dotNumerator;
float dotDenominator;
Vector3 vector;
intersection = Vector3.zero;
//calculate the distance between the linePoint and the line-plane intersection point
dotNumerator = Vector3.Dot((plane.Point - ray.origin), plane.Normal);
dotDenominator = Vector3.Dot(ray.direction, plane.Normal);
//line and plane are not parallel
if (dotDenominator != 0.0f)
{
length = dotNumerator / dotDenominator;
//create a vector from the linePoint to the intersection point
vector = ExtVector3.SetVectorLength(ray.direction, length);
//get the coordinates of the line-plane intersection point
intersection = ray.origin + vector;
return(true);
}
//output not valid
else
{
return(false);
}
}
/// <summary>
/// Return the closest point on the disc from k
/// </summary>
public bool GetClosestPointOnDisc(Vector3 k, ref Vector3 closestPoint)
{
closestPoint = Vector3.zero;
if (!AllowBottom && !_plane.IsAbove(k))
{
return(false);
}
//project point to a plane
Vector3 kProjected = ExtPlane.ProjectPointInPlane(_plane, k);
//if dist² < radius², this projected point is inside the circle
float distSquared = (kProjected - _plane.Point).sqrMagnitude;
bool isInsideShape = distSquared < _radiusSquared;
if (isInsideShape)
{
closestPoint = kProjected;
}
else
{
closestPoint = _plane.Point + (kProjected - _plane.Point).FastNormalized() * _radius;
}
return(true);
}
/// <summary>
/// get intersection between line and plane
/// </summary>
/// <param name="rayVector"></param>
/// <param name="rayPoint"></param>
/// <param name="plane"></param>
/// <returns></returns>
public static Vector3 PlaneLineIntersection(Ray ray, ExtPlane plane)
{
var diff = ray.origin - plane.Point;
var prod1 = Vector3.Dot(diff, plane.Normal);
var prod2 = Vector3.Dot(ray.direction, plane.Normal);
var prod3 = prod1 / prod2;
return(ray.origin - ray.direction * prod3);
}
/// <summary>
/// return the closest point on the circle from k
/// </summary>
/// <param name="k"></param>
/// <returns></returns>
public Vector3 GetClosestPointOnCircle(Vector3 k)
{
//project point to a plane
Vector3 kProjected = ExtPlane.ProjectPointInPlane(_plane, k);
//return the closest point on the circle
Vector3 pointExtremity = _plane.Point + (kProjected - _plane.Point).FastNormalized() * _radius;
return(pointExtremity);
}
/// <summary>
/// assume k is NOT on the same plane as the circle, we first do a projection
/// √( | xp−xc |² +| yp−yc |²) < r
/// </summary>
/// <param name="k"></param>
/// <returns></returns>
public bool IsInsideShapeWithProjection(Vector3 k)
{
if (!AllowBottom && !_plane.IsAbove(k))
{
return(false);
}
Vector3 kProjected = ExtPlane.ProjectPointInPlane(_plane, k);
float distSquared = (kProjected - _plane.Point).sqrMagnitude;
return(distSquared < _radiusSquared);
}
public static Vector3 ProjectPointInPlane(ExtPlane plane, Vector3 pointToProject)
{
return(pointToProject - (Vector3.Project(pointToProject - plane.Point, plane.Normal.normalized)));
}
public static bool PlanePlaneIntersection(ExtPlane plane1, ExtPlane plane2, out Vector3 linePoint, out Vector3 lineVec)
{
return(PlanePlaneIntersection(plane1.Point, plane1.Normal, plane2.Point, plane2.Normal, out linePoint, out lineVec));
}