/// <summary>
/// Checks a ray against a circle with a given origin and square radius.
/// </summary>
internal static bool CircleRayCast(
VoltShape shape,
Vector2 shapeOrigin,
float sqrRadius,
ref VoltRayCast ray,
ref VoltRayResult result)
{
Vector2 toOrigin = shapeOrigin - ray.origin;
if (toOrigin.sqrMagnitude < sqrRadius)
{
result.SetContained(shape);
return true;
}
float slope = Vector2.Dot(toOrigin, ray.direction);
if (slope < 0)
return false;
float sqrSlope = slope * slope;
float d = sqrRadius + sqrSlope - Vector2.Dot(toOrigin, toOrigin);
if (d < 0)
return false;
float dist = slope - Mathf.Sqrt(d);
if (dist < 0 || dist > ray.distance)
return false;
// N.B.: For historical raycasts this normal will be wrong!
// Must be either transformed back to world or invalidated later.
Vector2 normal = (dist * ray.direction - toOrigin).normalized;
result.Set(shape, dist, normal);
return true;
}
/// <summary>
/// Checks a ray against a circle with a given origin and square radius.
/// </summary>
internal static bool CircleRayCast(
VoltShape shape,
Vector2 shapeOrigin,
float sqrRadius,
ref VoltRayCast ray,
ref VoltRayResult result)
{
Vector2 toOrigin = shapeOrigin - ray.origin;
if (toOrigin.sqrMagnitude < sqrRadius)
{
result.SetContained(shape);
return(true);
}
float slope = Vector2.Dot(toOrigin, ray.direction);
if (slope < 0)
{
return(false);
}
float sqrSlope = slope * slope;
float d = sqrRadius + sqrSlope - Vector2.Dot(toOrigin, toOrigin);
if (d < 0)
{
return(false);
}
float dist = slope - Mathf.Sqrt(d);
if (dist < 0 || dist > ray.distance)
{
return(false);
}
// N.B.: For historical raycasts this normal will be wrong!
// Must be either transformed back to world or invalidated later.
Vector2 normal = (dist * ray.direction - toOrigin).normalized;
result.Set(shape, dist, normal);
return(true);
}
private bool CircleCastEdges(
ref VoltRayCast bodySpaceRay,
float radius,
ref VoltRayResult result)
{
int foundIndex = -1;
bool couldBeContained = true;
// Pre-compute and initialize values
float shortestDist = float.MaxValue;
Vector2 v3 = bodySpaceRay.direction.Left();
// Check the edges -- this will be different from the raycast because
// we care about staying within the ends of the edge line segment
for (int i = 0; i < this.countBody; i++)
{
Axis curAxis = this.bodyAxes[i];
// Push the edges out by the radius
Vector2 extension = curAxis.Normal * radius;
Vector2 a = this.bodyVertices[i] + extension;
Vector2 b = this.bodyVertices[(i + 1) % this.countBody] + extension;
// Update the check for containment
if (couldBeContained == true)
{
float proj =
Vector2.Dot(curAxis.Normal, bodySpaceRay.origin) - curAxis.Width;
// The point lies outside of the outer layer
if (proj > radius)
{
couldBeContained = false;
}
// The point lies between the outer and inner layer
else if (proj > 0.0f)
{
// See if the point is within the center Vornoi region of the edge
float d = VoltMath.Cross(curAxis.Normal, bodySpaceRay.origin);
if (d > VoltMath.Cross(curAxis.Normal, a))
{
couldBeContained = false;
}
if (d < VoltMath.Cross(curAxis.Normal, b))
{
couldBeContained = false;
}
}
}
// For the cast, only consider rays pointing towards the edge
if (Vector2.Dot(curAxis.Normal, bodySpaceRay.direction) >= 0.0f)
{
continue;
}
// See:
// https://rootllama.wordpress.com/2014/06/20/ray-line-segment-intersection-test-in-2d/
Vector2 v1 = bodySpaceRay.origin - a;
Vector2 v2 = b - a;
float denominator = Vector2.Dot(v2, v3);
float t1 = VoltMath.Cross(v2, v1) / denominator;
float t2 = Vector2.Dot(v1, v3) / denominator;
if ((t2 >= 0.0f) && (t2 <= 1.0f) && (t1 > 0.0f) && (t1 < shortestDist))
{
// See if the point is outside of any of the axes
shortestDist = t1;
foundIndex = i;
}
}
// Report results
if (couldBeContained == true)
{
result.SetContained(this);
return(true);
}
else if (foundIndex >= 0 && shortestDist <= bodySpaceRay.distance)
{
result.Set(
this,
shortestDist,
this.bodyAxes[foundIndex].Normal);
return(true);
}
return(false);
}
protected override bool ShapeRayCast(
ref VoltRayCast bodySpaceRay,
ref VoltRayResult result)
{
int foundIndex = -1;
float inner = float.MaxValue;
float outer = 0;
bool couldBeContained = true;
for (int i = 0; i < this.countBody; i++)
{
Axis curAxis = this.bodyAxes[i];
// Distance between the ray origin and the axis/edge along the
// normal (i.e., shortest distance between ray origin and the edge)
float proj =
Vector2.Dot(curAxis.Normal, bodySpaceRay.origin) - curAxis.Width;
// See if the point is outside of any of the axes
if (proj > 0.0f)
{
couldBeContained = false;
}
// Projection of the ray direction onto the axis normal (use
// negative normal because we want to get the penetration length)
float slope = Vector2.Dot(-curAxis.Normal, bodySpaceRay.direction);
if (slope == 0.0f)
{
continue;
}
float dist = proj / slope;
// The ray is pointing opposite the edge normal (towards the edge)
if (slope > 0.0f)
{
if (dist > inner)
{
return(false);
}
if (dist > outer)
{
outer = dist;
foundIndex = i;
}
}
// The ray is pointing along the edge normal (away from the edge)
else
{
if (dist < outer)
{
return(false);
}
if (dist < inner)
{
inner = dist;
}
}
}
if (couldBeContained == true)
{
result.SetContained(this);
return(true);
}
else if (foundIndex >= 0 && outer <= bodySpaceRay.distance)
{
result.Set(
this,
outer,
this.bodyAxes[foundIndex].Normal);
return(true);
}
return(false);
}
private bool CircleCastEdges(
ref VoltRayCast bodySpaceRay,
float radius,
ref VoltRayResult result)
{
int foundIndex = -1;
bool couldBeContained = true;
// Pre-compute and initialize values
float shortestDist = float.MaxValue;
Vector2 v3 = bodySpaceRay.direction.Left();
// Check the edges -- this will be different from the raycast because
// we care about staying within the ends of the edge line segment
for (int i = 0; i < this.countBody; i++)
{
Axis curAxis = this.bodyAxes[i];
// Push the edges out by the radius
Vector2 extension = curAxis.Normal * radius;
Vector2 a = this.bodyVertices[i] + extension;
Vector2 b = this.bodyVertices[(i + 1) % this.countBody] + extension;
// Update the check for containment
if (couldBeContained == true)
{
float proj =
Vector2.Dot(curAxis.Normal, bodySpaceRay.origin) - curAxis.Width;
// The point lies outside of the outer layer
if (proj > radius)
{
couldBeContained = false;
}
// The point lies between the outer and inner layer
else if (proj > 0.0f)
{
// See if the point is within the center Vornoi region of the edge
float d = VoltMath.Cross(curAxis.Normal, bodySpaceRay.origin);
if (d > VoltMath.Cross(curAxis.Normal, a))
couldBeContained = false;
if (d < VoltMath.Cross(curAxis.Normal, b))
couldBeContained = false;
}
}
// For the cast, only consider rays pointing towards the edge
if (Vector2.Dot(curAxis.Normal, bodySpaceRay.direction) >= 0.0f)
continue;
// See:
// https://rootllama.wordpress.com/2014/06/20/ray-line-segment-intersection-test-in-2d/
Vector2 v1 = bodySpaceRay.origin - a;
Vector2 v2 = b - a;
float denominator = Vector2.Dot(v2, v3);
float t1 = VoltMath.Cross(v2, v1) / denominator;
float t2 = Vector2.Dot(v1, v3) / denominator;
if ((t2 >= 0.0f) && (t2 <= 1.0f) && (t1 > 0.0f) && (t1 < shortestDist))
{
// See if the point is outside of any of the axes
shortestDist = t1;
foundIndex = i;
}
}
// Report results
if (couldBeContained == true)
{
result.SetContained(this);
return true;
}
else if (foundIndex >= 0 && shortestDist <= bodySpaceRay.distance)
{
result.Set(
this,
shortestDist,
this.bodyAxes[foundIndex].Normal);
return true;
}
return false;
}
protected override bool ShapeRayCast(
ref VoltRayCast bodySpaceRay,
ref VoltRayResult result)
{
int foundIndex = -1;
float inner = float.MaxValue;
float outer = 0;
bool couldBeContained = true;
for (int i = 0; i < this.countBody; i++)
{
Axis curAxis = this.bodyAxes[i];
// Distance between the ray origin and the axis/edge along the
// normal (i.e., shortest distance between ray origin and the edge)
float proj =
Vector2.Dot(curAxis.Normal, bodySpaceRay.origin) - curAxis.Width;
// See if the point is outside of any of the axes
if (proj > 0.0f)
couldBeContained = false;
// Projection of the ray direction onto the axis normal (use
// negative normal because we want to get the penetration length)
float slope = Vector2.Dot(-curAxis.Normal, bodySpaceRay.direction);
if (slope == 0.0f)
continue;
float dist = proj / slope;
// The ray is pointing opposite the edge normal (towards the edge)
if (slope > 0.0f)
{
if (dist > inner)
{
return false;
}
if (dist > outer)
{
outer = dist;
foundIndex = i;
}
}
// The ray is pointing along the edge normal (away from the edge)
else
{
if (dist < outer)
{
return false;
}
if (dist < inner)
{
inner = dist;
}
}
}
if (couldBeContained == true)
{
result.SetContained(this);
return true;
}
else if (foundIndex >= 0 && outer <= bodySpaceRay.distance)
{
result.Set(
this,
outer,
this.bodyAxes[foundIndex].Normal);
return true;
}
return false;
}
