/// <summary>Computes the inverse of the matrix.</summary>
/// <returns>The inverse matrix</returns>
public Matrix2D Inverse()
{
Matrix2D invMat = new Matrix2D();
float det = this[0, 0] * this[1, 1] - this[0, 1] * this[1, 0];
if (Mathf.Approximately(0.0f, det))
{
return(zero);
}
float invDet = 1.0F / det;
invMat[0, 0] = this[1, 1] * invDet;
invMat[0, 1] = -this[0, 1] * invDet;
invMat[1, 0] = -this[1, 0] * invDet;
invMat[1, 1] = this[0, 0] * invDet;
// Do the translation part
invMat[0, 2] = -(this[0, 2] * invMat[0, 0] + this[1, 2] * invMat[0, 1]);
invMat[1, 2] = -(this[0, 2] * invMat[1, 0] + this[1, 2] * invMat[1, 1]);
return(invMat);
}
static void GenerateTip(BezierSegment segment, bool atStart, float t, PathEnding ending, float halfThickness, TessellationOptions tessellateOptions, List <Vector2> verts, List <UInt16> inds)
{
// The tip includes the vertices at the end itself
Vector2 tan, nrm;
var pos = VectorUtils.EvalFull(segment, t, out tan, out nrm);
int indexStart = verts.Count;
switch (ending)
{
case PathEnding.Chop:
if (atStart)
{
verts.Add(pos + nrm * halfThickness);
verts.Add(pos - nrm * halfThickness);
}
else
{
// Not much, path segments are always expected to be generated perpendicular to the path
// at the segment point location, so we don't have to do anything for the ending
}
break;
case PathEnding.Square:
if (atStart)
{
verts.Add(pos + nrm * halfThickness - tan * halfThickness);
verts.Add(pos - nrm * halfThickness - tan * halfThickness);
verts.Add(pos + nrm * halfThickness);
verts.Add(pos - nrm * halfThickness);
inds.Add((UInt16)(indexStart + 0));
inds.Add((UInt16)(indexStart + 3));
inds.Add((UInt16)(indexStart + 1));
inds.Add((UInt16)(indexStart + 0));
inds.Add((UInt16)(indexStart + 2));
inds.Add((UInt16)(indexStart + 3));
}
else
{
// Relying on the last two vertices, and just adding two of our own here
verts.Add(pos + nrm * halfThickness + tan * halfThickness);
verts.Add(pos - nrm * halfThickness + tan * halfThickness);
inds.Add((UInt16)(indexStart + 0 - 2));
inds.Add((UInt16)(indexStart + 3 - 2));
inds.Add((UInt16)(indexStart + 1 - 2));
inds.Add((UInt16)(indexStart + 0 - 2));
inds.Add((UInt16)(indexStart + 2 - 2));
inds.Add((UInt16)(indexStart + 3 - 2));
}
break;
case PathEnding.Round:
float arcSign = atStart ? -1 : 1;
int arcSegments = CalculateArcSteps(halfThickness, 0, Mathf.PI, tessellateOptions);
for (int i = 1; i < arcSegments; i++)
{
float angle = Mathf.PI * (i / (float)arcSegments);
verts.Add(pos + Matrix2D.RotateLH(angle) * nrm * halfThickness * arcSign);
}
if (atStart)
{
// Note how we maintain the last two vertices being setup for connection by the rest of the path vertices
int indexTipStart = verts.Count;
verts.Add(pos + nrm * halfThickness);
verts.Add(pos - nrm * halfThickness);
for (int i = 1; i < arcSegments; i++)
{
inds.Add((UInt16)(indexTipStart + 1));
inds.Add((UInt16)(indexStart + i - 1));
inds.Add((UInt16)(indexStart + i));
}
}
else
{
inds.Add((UInt16)(indexStart - 1));
inds.Add((UInt16)(indexStart - 2));
inds.Add((UInt16)(indexStart + 0));
for (int i = 1; i < arcSegments - 1; i++)
{
inds.Add((UInt16)(indexStart - 1));
inds.Add((UInt16)(indexStart + i - 1));
inds.Add((UInt16)(indexStart + i));
}
}
break;
default:
System.Diagnostics.Debug.Assert(false); // Joining has its own function
break;
}
}
static void GenerateJoining(JoiningInfo joinInfo, PathCorner corner, float halfThickness, float tippedCornerLimit, TessellationOptions tessellateOptions, List <Vector2> verts, List <UInt16> inds)
{
// The joining generates the vertices at both ends as well as the joining itself
if (verts.Count == 0)
{
// Starting a path with a joining (meaning a loop)
verts.Add(joinInfo.RoundPosThickness ? joinInfo.PosThicknessEnd : joinInfo.InnerCornerVertex);
verts.Add(joinInfo.RoundPosThickness ? joinInfo.InnerCornerVertex : joinInfo.NegThicknessEnd);
}
System.Diagnostics.Debug.Assert(verts.Count >= 2);
int indexStart = verts.Count - 2; // Using the last two vertices
// Convert a tipped corner to a beveled one if tippedCornerLimit ratio is reached
if (corner == PathCorner.Tipped && tippedCornerLimit >= 1.0f)
{
var theta = Vector2.Angle(-joinInfo.TanAtEnd, joinInfo.TanAtStart) * Mathf.Deg2Rad;
var ratio = 1.0f / Mathf.Sin(theta / 2.0f);
if (ratio > tippedCornerLimit)
{
corner = PathCorner.Beveled;
}
}
if (joinInfo.SimpleJoin)
{
// TODO
}
else if (corner == PathCorner.Tipped)
{
verts.Add(joinInfo.PosThicknessClosingPoint);
verts.Add(joinInfo.NegThicknessClosingPoint);
verts.Add(joinInfo.RoundPosThickness ? joinInfo.PosThicknessStart : joinInfo.InnerCornerVertex);
verts.Add(joinInfo.RoundPosThickness ? joinInfo.InnerCornerVertex : joinInfo.NegThicknessStart);
// Ending to tip
inds.Add((UInt16)(indexStart + 0));
inds.Add((UInt16)(indexStart + 3));
inds.Add((UInt16)(indexStart + 1));
inds.Add((UInt16)(indexStart + 0));
inds.Add((UInt16)(indexStart + 2));
inds.Add((UInt16)(indexStart + 3));
// Tip to starting
inds.Add((UInt16)(indexStart + 4));
inds.Add((UInt16)(indexStart + 3));
inds.Add((UInt16)(indexStart + 2));
inds.Add((UInt16)(indexStart + 4));
inds.Add((UInt16)(indexStart + 5));
inds.Add((UInt16)(indexStart + 3));
return;
}
else if (corner == PathCorner.Beveled)
{
verts.Add(joinInfo.RoundPosThickness ? joinInfo.PosThicknessEnd : joinInfo.InnerCornerVertex); // 2
verts.Add(joinInfo.RoundPosThickness ? joinInfo.InnerCornerVertex : joinInfo.NegThicknessEnd); // 3
verts.Add(joinInfo.RoundPosThickness ? joinInfo.PosThicknessStart : joinInfo.InnerCornerVertex); // 4
verts.Add(joinInfo.RoundPosThickness ? joinInfo.InnerCornerVertex : joinInfo.NegThicknessStart); // 5
// Ending to tip
inds.Add((UInt16)(indexStart + 0));
inds.Add((UInt16)(indexStart + 2));
inds.Add((UInt16)(indexStart + 1));
inds.Add((UInt16)(indexStart + 1));
inds.Add((UInt16)(indexStart + 2));
inds.Add((UInt16)(indexStart + 3));
// Bevel
if (joinInfo.RoundPosThickness)
{
inds.Add((UInt16)(indexStart + 2));
inds.Add((UInt16)(indexStart + 4));
inds.Add((UInt16)(indexStart + 3));
}
else
{
inds.Add((UInt16)(indexStart + 3));
inds.Add((UInt16)(indexStart + 2));
inds.Add((UInt16)(indexStart + 5));
}
return;
}
if (corner == PathCorner.Round)
{
float sweepAngle = Mathf.Acos(Vector2.Dot(joinInfo.NormAtEnd, joinInfo.NormAtStart));
bool flipArc = false;
if (!PointOnTheLeftOfLine(Vector2.zero, joinInfo.NormAtEnd, joinInfo.NormAtStart))
{
sweepAngle = -sweepAngle;
flipArc = true;
}
UInt16 innerCornerVertexIndex = (UInt16)verts.Count;
verts.Add(joinInfo.InnerCornerVertex);
int arcSegments = CalculateArcSteps(halfThickness, 0, sweepAngle, tessellateOptions);
for (int i = 0; i <= arcSegments; i++)
{
float angle = sweepAngle * (i / (float)arcSegments);
Vector2 nrm = Matrix2D.RotateLH(angle) * joinInfo.NormAtEnd;
if (flipArc)
{
nrm = -nrm;
}
verts.Add(nrm * halfThickness + joinInfo.JoinPos);
if (i == 0)
{
inds.Add((UInt16)(indexStart + 0));
inds.Add((UInt16)(indexStart + 3));
inds.Add((UInt16)(indexStart + (joinInfo.RoundPosThickness ? 2 : 1)));
inds.Add((UInt16)(indexStart + 0));
inds.Add((UInt16)(indexStart + 2));
inds.Add((UInt16)(indexStart + (joinInfo.RoundPosThickness ? 1 : 3)));
}
else
{
if (joinInfo.RoundPosThickness)
{
inds.Add((UInt16)(indexStart + i + (flipArc ? 3 : 2)));
inds.Add((UInt16)(indexStart + i + (flipArc ? 2 : 3)));
inds.Add(innerCornerVertexIndex);
}
else
{
inds.Add((UInt16)(indexStart + i + (flipArc ? 3 : 2)));
inds.Add((UInt16)(indexStart + i + (flipArc ? 2 : 3)));
inds.Add(innerCornerVertexIndex);
}
}
}
// Manually add the last segment, maintain the expected vertex positioning
int endingVerticesIndex = verts.Count;
if (joinInfo.RoundPosThickness)
{
verts.Add(joinInfo.PosThicknessStart);
verts.Add(joinInfo.InnerCornerVertex);
}
else
{
verts.Add(joinInfo.InnerCornerVertex);
verts.Add(joinInfo.NegThicknessStart);
}
inds.Add((UInt16)(endingVerticesIndex - 1));
inds.Add((UInt16)(endingVerticesIndex + 0));
inds.Add(innerCornerVertexIndex);
}
}
#pragma warning disable 612, 618 // Silence use of deprecated IDrawable
private static List <Geometry> TessellateNodeHierarchyRecursive(SceneNode node, TessellationOptions tessellationOptions, Matrix2D worldTransform, float worldOpacity, Dictionary <SceneNode, float> nodeOpacities)
{
if (node.Clipper != null)
{
VectorClip.PushClip(TraceNodeHierarchyShapes(node.Clipper, tessellationOptions), worldTransform);
}
var geoms = new List <Geometry>();
if (node.Drawables != null)
{
// We process the drawables even though they are obsolete, until we remove the IDrawable interface entirely
foreach (var drawable in node.Drawables)
{
var vectorShape = drawable as Shape;
if (vectorShape != null)
{
bool isConvex = vectorShape.IsConvex && vectorShape.Contours.Length == 1;
TessellateShape(vectorShape, geoms, tessellationOptions, isConvex);
continue;
}
var vectorPath = drawable as Path;
if (vectorPath != null)
{
TessellatePath(vectorPath.Contour, vectorPath.PathProps, geoms, tessellationOptions);
continue;
}
var vectorRect = drawable as Rectangle;
if (vectorRect != null)
{
TessellateRectangle(vectorRect, geoms, tessellationOptions);
continue;
}
}
}
if (node.Shapes != null)
{
foreach (var shape in node.Shapes)
{
bool isConvex = shape.IsConvex && shape.Contours.Length == 1;
TessellateShape(shape, geoms, tessellationOptions, isConvex);
}
}
foreach (var g in geoms)
{
g.Color.a *= worldOpacity;
g.WorldTransform = worldTransform;
g.UnclippedBounds = Bounds(g.Vertices);
VectorClip.ClipGeometry(g);
}
if (node.Children != null)
{
foreach (var child in node.Children)
{
var childOpacity = 1.0f;
if (nodeOpacities == null || !nodeOpacities.TryGetValue(child, out childOpacity))
{
childOpacity = 1.0f;
}
var transform = worldTransform * child.Transform;
var opacity = worldOpacity * childOpacity;
var childGeoms = TessellateNodeHierarchyRecursive(child, tessellationOptions, transform, opacity, nodeOpacities);
geoms.AddRange(childGeoms);
}
}
if (node.Clipper != null)
{
VectorClip.PopClip();
}
return(geoms);
}
internal static Vector2[] GenerateShapeUVs(Vector2[] verts, Rect bounds, Matrix2D uvTransform)
{
UnityEngine.Profiling.Profiler.BeginSample("GenerateShapeUVs");
uvTransform =
Matrix2D.Translate(new Vector2(0, 1)) * Matrix2D.Scale(new Vector2(1.0f, -1.0f)) * // Do 1-uv.y
uvTransform *
Matrix2D.Scale(new Vector2(1.0f / bounds.width, 1.0f / bounds.height)) * Matrix2D.Translate(-bounds.position);
var uvs = new Vector2[verts.Length];
int vertCount = verts.Length;
for (int i = 0; i < vertCount; i++)
{
uvs[i] = uvTransform * verts[i];
}
UnityEngine.Profiling.Profiler.EndSample();
return(uvs);
}
#pragma warning disable 612, 618 // Silence use of deprecated IDrawable
private static List <Geometry> TessellateNodeHierarchyRecursive(SceneNode node, TessellationOptions tessellationOptions, Matrix2D worldTransform, float worldOpacity, Dictionary <SceneNode, float> nodeOpacities)
{
if (node.Clipper != null)
{
VectorClip.PushClip(TraceNodeHierarchyShapes(node.Clipper, tessellationOptions), worldTransform);
}
var geoms = new List <Geometry>();
if (node.Shapes != null)
{
foreach (var shape in node.Shapes)
{
bool isConvex = shape.IsConvex && shape.Contours.Length == 1;
TessellateShape(shape, geoms, tessellationOptions, isConvex);
}
}
foreach (var g in geoms)
{
g.Color.a *= worldOpacity;
g.WorldTransform = worldTransform;
g.UnclippedBounds = Bounds(g.Vertices);
VectorClip.ClipGeometry(g);
}
if (node.Children != null)
{
foreach (var child in node.Children)
{
var childOpacity = 1.0f;
if (nodeOpacities == null || !nodeOpacities.TryGetValue(child, out childOpacity))
{
childOpacity = 1.0f;
}
var transform = worldTransform * child.Transform;
var opacity = worldOpacity * childOpacity;
var childGeoms = TessellateNodeHierarchyRecursive(child, tessellationOptions, transform, opacity, nodeOpacities);
geoms.AddRange(childGeoms);
}
}
if (node.Clipper != null)
{
VectorClip.PopClip();
}
return(geoms);
}