/// <summary>Adds an arc between the given points using the pen point as a control point.
/// Note that nothing will be seen until you call a fill or stroke method.</summary>
public void arcTo(float x1, float y1, float x2, float y2, float radius)
{
VectorPoint previous = Path.LatestPathNode;
float x0;
float y0;
if (previous == null)
{
x0 = 0f;
y0 = 0f;
}
else
{
x0 = previous.X;
y0 = previous.Y;
}
// How this works:
// Line from 0->1.
// Another from 2->1, thus forming a 'triangle'.
// Slide a circle of the given radius in this triangle such that it's
// as far in as it will go whilst just touching both lines.
// Draw an arc from the two intersection points of the circle with the triangle.
// What we need to find:
// - Circle center.
// - The start and end angles. Always clockwise.
// Create the new arc node:
ArcLinePoint arcNode = new ArcLinePoint(x2, y2);
// Apply the radius:
arcNode.Radius = radius;
// First find the angle of 1 from +ve x. This is just an Atan2 call:
float angleLine2 = (float)Math.Atan2(y0 - y1, x0 - x1);
// Find the angle of 2 relative to 1.
// As we know the angle of 1 relative to +ve x, we can find 1 relative to +ve x
// and then grab the difference.
float rotateThrough = (float)Math.Atan2(y2 - y1, x2 - x1) - angleLine2;
// Find half of the angle:
float halfAngle = rotateThrough / 2f;
// What's the distance of point 1 to the circle center?
float distanceToCenter = radius / (float)Math.Cos(halfAngle);
// Resolve the x coordinate of the center:
arcNode.CircleCenterX = (distanceToCenter * (float)Math.Cos(halfAngle - angleLine2)) + x1;
// Resolve the y coordinate of the center:
arcNode.CircleCenterY = (distanceToCenter * (float)Math.Sin(halfAngle - angleLine2)) + y1;
// Apply the angles:
arcNode.StartAngle = -rotateThrough - angleLine2;
arcNode.EndAngle = arcNode.StartAngle - rotateThrough;
float arcStartNodeX;
float arcStartNodeY;
arcNode.SampleAt(0f, out arcStartNodeX, out arcStartNodeY);
float arcEndNodeX;
float arcEndNodeY;
arcNode.SampleAt(1f, out arcEndNodeX, out arcEndNodeY);
if (Path.FirstPathNode == null)
{
// This occurs if the arc is the first thing we draw. No line is drawn to it.
Path.MoveTo(arcStartNodeX, arcStartNodeY);
}
else if (x0 != arcStartNodeX || y0 != arcStartNodeY)
{
Path.LineTo(arcStartNodeX, arcStartNodeY);
}
// Apply the node location:
arcNode.X = arcEndNodeX;
arcNode.Y = arcEndNodeY;
// Add the other end:
Path.AddPathNode(arcNode);
}
/// <summary>Creates an arc around the given circle center. Note that nothing will
/// be seen until you call a fill or stroke method.</summary>
public void arc(float centerX, float centerY, float radius, float sAngle, float eAngle, bool counterClockwise)
{
VectorPoint previous = Path.LatestPathNode;
float x0;
float y0;
if (previous == null)
{
x0 = 0f;
y0 = 0f;
}
else
{
x0 = previous.X;
y0 = previous.Y;
}
// Clockwise eAngle > sAngle; counter clockwise otherwise.
if (eAngle > sAngle)
{
if (counterClockwise)
{
// Get them both in range:
eAngle = eAngle % (Mathf.PI * 2f);
sAngle = sAngle % (Mathf.PI * 2f);
// Reduce eAngle by a full rotation so it's smaller:
eAngle -= (Mathf.PI * 2f);
}
}
else if (!counterClockwise)
{
// Get them both in range:
eAngle = eAngle % (Mathf.PI * 2f);
sAngle = sAngle % (Mathf.PI * 2f);
// Reduce sAngle by a full rotation so it's smaller:
sAngle -= (Mathf.PI * 2f);
}
// First, figure out where the actual start is.
// It's radius units to the right of center, then rotated through radius around center.
// Thus we have a triangle with hyp length of 'radius' and an angle of sAngle:
float startX = radius * (float)Math.Cos(sAngle);
float startY = radius * (float)Math.Sin(sAngle);
// Now find the end point, using exactly the same method:
float endX = radius * (float)Math.Cos(eAngle);
float endY = radius * (float)Math.Sin(eAngle);
// We now have an arc from the current position to endX/endY.
// The start and exit node angles are usefully just offset from the given ones.
// This is because an sAngle of zero should create an arc which starts travelling downwards.
// (Or upwards if it's counter clockwise):
// Where does the arc start from?
float arcStartX = centerX + startX;
float arcStartY = centerY + startY;
if (Path.FirstPathNode == null)
{
// This occurs if the arc is the first thing we draw. No line is drawn to it.
Path.MoveTo(arcStartX, arcStartY);
}
else if (arcStartX != x0 || arcStartY != y0)
{
// Draw a line to this point:
Path.LineTo(arcStartX, arcStartY);
}
// Create the new arc node:
ArcLinePoint arcNode = new ArcLinePoint(centerX + endX, centerY + endY);
// Apply the radius:
arcNode.Radius = radius;
// Apply the angles:
arcNode.StartAngle = sAngle;
arcNode.EndAngle = eAngle;
// Apply the center:
arcNode.CircleCenterX = centerX;
arcNode.CircleCenterY = centerY;
// Add the other end:
Path.AddPathNode(arcNode);
}
