public static List <Vector3> GenerateSphereBorderPoints(Camera camera, Vector3 sphereCenter, float sphereRadius, int numPoints)
{
if (numPoints < 3)
{
return(new List <Vector3>());
}
Transform cameraTransform = camera.transform;
List <Vector3> borderPoints = Generate3DCircleBorderPoints(sphereCenter, sphereRadius, cameraTransform.right, cameraTransform.up, numPoints);
for (int ptIndex = 0; ptIndex < numPoints; ++ptIndex)
{
Vector3 borderPt = borderPoints[ptIndex];
Vector3 borderNormal = (borderPt - sphereCenter).normalized;
Vector3 cameraRay = (borderPt - cameraTransform.position).normalized;
if (camera.orthographic)
{
cameraRay = cameraTransform.forward;
}
float dot = Vector3.Dot(borderNormal, cameraRay);
if (Mathf.Abs(dot) > 1e-5f)
{
float angle = MathEx.SafeAcos(dot) * Mathf.Rad2Deg;
Vector3 rotationAxis = Vector3.Cross(cameraRay, borderNormal).normalized;
Quaternion rotation = Quaternion.AngleAxis(90.0f - angle, rotationAxis);
borderNormal = (rotation * borderNormal).normalized;
borderPoints[ptIndex] = sphereCenter + borderNormal * sphereRadius;
}
}
return(borderPoints);
}
public static List <Vector3> GenerateSphereBorderPoints(Camera camera, Vector3 sphereCenter, float sphereRadius, int numPoints)
{
if (numPoints < 3)
{
return(new List <Vector3>());
}
Transform cameraTransform = camera.transform;
Plane cullPlane = new Plane(cameraTransform.forward, cameraTransform.position);
List <Vector3> borderPoints = Generate3DCircleBorderPoints(sphereCenter, sphereRadius, cameraTransform.right, cameraTransform.up, numPoints);
for (int ptIndex = 0; ptIndex < numPoints; ++ptIndex)
{
Vector3 borderPt = borderPoints[ptIndex];
Vector3 borderNormal = (borderPt - sphereCenter).normalized;
Vector3 cameraRay = (borderPt - cameraTransform.position).normalized;
if (camera.orthographic)
{
cameraRay = cameraTransform.forward;
}
float dot = Vector3.Dot(borderNormal, cameraRay);
if (Mathf.Abs(dot) > 1e-5f)
{
float angle = MathEx.SafeAcos(dot) * Mathf.Rad2Deg;
Vector3 rotationAxis = Vector3.Cross(cameraRay, borderNormal).normalized;
Quaternion rotation = Quaternion.AngleAxis(90.0f - angle, rotationAxis);
borderNormal = (rotation * borderNormal).normalized;
borderPoints[ptIndex] = sphereCenter + borderNormal * sphereRadius;
// Note: Reject if any point lies behind the camera. In that case, we get
// invalid points when converted by the client in screen space.
if (cullPlane.GetDistanceToPoint(borderPoints[ptIndex]) < 0.0f)
{
return(new List <Vector3>());
}
}
}
return(borderPoints);
}
public static Quaternion FromToRotation2D(Vector2 from, Vector2 to)
{
from = from.normalized;
to = to.normalized;
float dot = Vector2.Dot(from, to);
if (1.0f - dot < 1e-5f)
{
return(Quaternion.identity);
}
if (1.0f + dot < 1e-5f)
{
return(Quaternion.AngleAxis(180.0f, Vector3.forward));
}
float angle = MathEx.SafeAcos(dot) * Mathf.Rad2Deg;
Vector3 rotationAxis = Vector3.Cross(from, to).normalized;
return(Quaternion.AngleAxis(angle, rotationAxis));
}
// Unity versions below 2017 don't have Vector3.SignedAngle
public static float SignedAngle(Vector3 from, Vector3 to, Vector3 axis)
{
float dot = Vector3.Dot(from.normalized, to.normalized);
if ((1.0f - dot) < 1e-5f)
{
return(0.0f);
}
if ((1.0f + dot) < 1e-5f)
{
return(180.0f);
}
Vector3 cross = Vector3.Cross(from, to).normalized;
float angle = MathEx.SafeAcos(dot) * Mathf.Rad2Deg;
if (Vector3.Dot(cross, axis) < 0.0f)
{
angle = -angle;
}
return(angle);
}
