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darling-cocotron/Onyx2D/VGPath.m

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/*------------------------------------------------------------------------
*
* Derivative of the OpenVG 1.0.1 Reference Implementation
* -------------------------------------
*
* Copyright (c) 2007 The Khronos Group Inc.
*
* Permission is hereby granted, free of charge, to any person obtaining a
* copy of this software and /or associated documentation files
* (the "Materials "), to deal in the Materials without restriction,
* including without limitation the rights to use, copy, modify, merge,
* publish, distribute, sublicense, and/or sell copies of the Materials,
* and to permit persons to whom the Materials are furnished to do so,
* subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included
* in all copies or substantial portions of the Materials.
*
* THE MATERIALS ARE PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM,
* DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR
* OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE MATERIALS OR
* THE USE OR OTHER DEALINGS IN THE MATERIALS.
*
*-------------------------------------------------------------------*/
#import "VGPath.h"
#import <Onyx2D/VGmath.h>
static inline void RI_SWAP(O2Float *a, O2Float *b) { O2Float tmp = *a; *a = *b; *b = tmp; }
static inline O2Float RI_RAD_TO_DEG(O2Float a) { return (O2Float)(a * 180.0f/ M_PI); }
static inline O2Point Vector2Negate(O2Point result){
return O2PointMake(-result.x,-result.y);
}
static inline O2Float Vector2Length(O2Point v){
return sqrt((double)v.x*(double)v.x+(double)v.y*(double)v.y);
}
static inline BOOL Vector2IsEqual(O2Point v1,O2Point v2 ){
return (v1.x == v2.x) && (v1.y == v2.y);
}
static inline BOOL Vector2IsZero(O2Point v){
return (v.x == 0.0f) && (v.y == 0.0f);
}
static inline O2Point Vector2MultiplyByFloat(O2Point v,O2Float f){
return O2PointMake(v.x*f,v.y*f);
}
static inline O2Point Vector2Add(O2Point v1,O2Point v2 ){
return O2PointMake(v1.x+v2.x, v1.y+v2.y);
}
//if v is a zero vector, returns a zero vector
static inline O2Point Vector2Normalize(O2Point v){
double l = (double)v.x*(double)v.x+(double)v.y*(double)v.y;
if( l != 0.0 )
l = 1.0 / sqrt(l);
return O2PointMake((O2Float)((double)v.x * l), (O2Float)((double)v.y * l));
}
static inline O2Point Vector2PerpendicularCW(O2Point v){
return O2PointMake(v.y, -v.x);
}
static inline O2Point Vector2PerpendicularCCW(O2Point v){
return O2PointMake(-v.y, v.x);
}
static inline O2Point Vector2Perpendicular(O2Point v, BOOL cw){
if(cw)
return O2PointMake(v.y, -v.x);
return O2PointMake(-v.y, v.x);
}
enum VertexFlags {
START_SUBPATH = (1<<0),
END_SUBPATH = (1<<1),
START_SEGMENT = (1<<2),
END_SEGMENT = (1<<3),
CLOSE_SUBPATH = (1<<4),
IMPLICIT_CLOSE_SUBPATH = (1<<5)
};
typedef struct Vertex {
O2Point userPosition;
O2Point userTangent;
O2Float pathLength;
unsigned int flags;
} Vertex;
//data produced by tessellation
typedef struct VertexIndex {
int start;
int end;
} VertexIndex;
typedef struct {
O2Point p;
O2Point t;
O2Point ccw;
O2Point cw;
O2Float pathLength;
unsigned int flags;
BOOL inDash;
} StrokeVertex;
static inline StrokeVertex StrokeVertexInit(){
StrokeVertex result;
result.p=O2PointMake(0,0);
result.t=O2PointMake(0,0);
result.ccw=O2PointMake(0,0);
result.cw=O2PointMake(0,0);
result.pathLength=0;
result.flags=0;
result.inDash=NO;
return result;
}
#define RI_FLOAT_MAX FLT_MAX
/*-------------------------------------------------------------------*//*!
* \brief Form a reliable normalized average of the two unit input vectors.
* The average always lies to the given direction from the first
* vector.
* \param u0, u1 Unit input vectors.
* \param cw True if the average should be clockwise from u0, NO if
* counterclockwise.
* \return Average of the two input vectors.
* \note
*//*-------------------------------------------------------------------*/
static O2Point unitAverageWithDirection(O2Point u0, O2Point u1) {
O2Point u =Vector2MultiplyByFloat(Vector2Add(u0 , u1), 0.5f);
O2Point n0 = Vector2PerpendicularCCW(u0);
if( Vector2Dot(u, u) > 0.25f ){
//the average is long enough and thus reliable
if( Vector2Dot(n0, u1) < 0.0f )
u = Vector2Negate(u); //choose the larger angle
}
else {
// the average is too short, use the average of the normals to the vectors instead
O2Point n1 = Vector2PerpendicularCW(u1);
u = Vector2MultiplyByFloat(Vector2Add(n0 , n1), 0.5f);
}
u = Vector2Negate(u);
return Vector2Normalize(u);
}
/*-------------------------------------------------------------------*//*!
* \brief Form a reliable normalized average of the two unit input vectors.
* The average lies on the side where the angle between the input
* vectors is less than 180 degrees.
* \param u0, u1 Unit input vectors.
* \return Average of the two input vectors.
* \note
*//*-------------------------------------------------------------------*/
static O2Point unitAverage(O2Point u0, O2Point u1){
O2Point u =Vector2MultiplyByFloat(Vector2Add(u0 , u1), 0.5f);
if( Vector2Dot(u, u) < 0.25f ){
// the average is unreliable, use the average of the normals to the vectors instead
O2Point n0 = Vector2PerpendicularCCW(u0);
O2Point n1 = Vector2PerpendicularCW(u1);
u = Vector2MultiplyByFloat(Vector2Add(n0 , n1) , 0.5f);
if( Vector2Dot(n1, u0) < 0.0f )
u = Vector2Negate(u);
}
return Vector2Normalize(u);
}
// Interpolate the given unit tangent vectors to the given direction on a unit circle.
static O2Point circularLerpWithDirection(O2Point t0, O2Point t1, O2Float ratio) {
O2Point u0 = t0, u1 = t1;
O2Float l0 = 0.0f, l1 = 1.0f;
int i;
for(i=0;i<8;i++) {
O2Point n = unitAverageWithDirection(u0, u1);
O2Float l = 0.5f * (l0 + l1);
if( ratio < l ){
u1 = n;
l1 = l;
}
else {
u0 = n;
l0 = l;
}
}
return u0;
}
// Interpolate the given unit tangent vectors on a unit circle. Smaller angle between the vectors is used.
static O2Point circularLerp(O2Point t0, O2Point t1, O2Float ratio){
O2Point u0 = t0, u1 = t1;
O2Float l0 = 0.0f, l1 = 1.0f;
int i;
for(i=0;i<8;i++) {
O2Point n = unitAverage(u0, u1);
O2Float l = 0.5f * (l0 + l1);
if( ratio < l ){
u1 = n;
l1 = l;
}
else {
u0 = n;
l0 = l;
}
}
return u0;
}
@implementation VGPath
-initWithKGPath:(O2Path *)path {
_path=[path retain];
self->m_userMinx=0.0f;
self->m_userMiny=0.0f;
self->m_userMaxx=0.0f;
self->m_userMaxy=0.0f;
self->_vertexCount=0;
self->_vertexCapacity=2;
self->_vertices=NSZoneMalloc(NULL,self->_vertexCapacity*sizeof(Vertex));
self->_segmentToVertexCapacity=2;
self->_segmentToVertex=NSZoneMalloc(NULL,self->_segmentToVertexCapacity*sizeof(VertexIndex));
return self;
}
-(void)dealloc {
[_path release];
NSZoneFree(NULL,self->_vertices);
NSZoneFree(NULL,self->_segmentToVertex);
[super dealloc];
}
/// Given a path segment type, returns the number of coordinates it uses.
int O2PathElementTypeToNumCoordinates(O2PathElementType segment){
RI_ASSERT(((int)segment) >= 0 && ((int)segment) <= 4);
static const int coords[5] = {1,1,2,3,0};
return coords[(int)segment];
}
// Computes the number of coordinates a segment sequence uses.
int VGPathCountNumCoordinates(const uint8_t* segments, int numSegments){
RI_ASSERT(segments);
RI_ASSERT(numSegments >= 0);
int coordinates = 0;
int i;
for(i=0;i<numSegments;i++)
coordinates += O2PathElementTypeToNumCoordinates((O2PathElementType)segments[i]);
return coordinates;
}
// Tessellates a path for filling and appends resulting edges to a context.
void VGPathFill(VGPath *self,O2AffineTransform pathToSurface, O2Context_builtin *context){
VGPathTessellateIfNeeded(self);
O2Point p0=O2PointMake(0,0);
int i;
for(i=0;i<self->_vertexCount;i++){
O2Point p1 = O2PointApplyAffineTransform(self->_vertices[i].userPosition,pathToSurface );
if(!(self->_vertices[i].flags & START_SEGMENT)){
//in the middle of a segment
O2DContextAddEdge(context,p0, p1);
}
p0 = p1;
}
}
/* Smoothly interpolates between two StrokeVertices. Positions
are interpolated linearly, while tangents are interpolated
on a unit circle. Stroking is implemented so that overlapping
geometry doesnt cancel itself when filled with nonzero rule.
The resulting polygons are closed. */
static inline O2Point O2PointApplyAffineTransformNoTranslate(O2Point point,O2AffineTransform xform){
O2Point result;
result.x=xform.a*point.x+xform.c*point.y;
result.y=xform.b*point.x+xform.d*point.y;
return result;
}
void VGPathInterpolateStroke(O2AffineTransform pathToSurface, O2Context_builtin *context,StrokeVertex v0,StrokeVertex v1, O2Float strokeWidth){
O2Point ppccw = O2PointApplyAffineTransform(v0.ccw,pathToSurface);
O2Point ppcw = O2PointApplyAffineTransform(v0.cw,pathToSurface);
O2Point endccw = O2PointApplyAffineTransform(v1.ccw,pathToSurface);
O2Point endcw = O2PointApplyAffineTransform(v1.cw,pathToSurface);
const O2Float tessellationAngle = 5.0f;
O2Float angle = RI_RAD_TO_DEG((O2Float)acos(RI_CLAMP(Vector2Dot(v0.t, v1.t), -1.0f, 1.0f))) / tessellationAngle;
int samples = RI_INT_MAX((int)ceil(angle), 1);
O2Point pnccw = ppccw;
O2Point pncw = ppcw;
if(samples==1){
/* If there is only one sample then the line is close to straight, we use the tangent of one of the vertices
instead of interpolating and just make a box.
*/
// O2Float t = 1;
// O2Point tangent = circularLerp(v0.t, v1.t, t);
O2Point v0p=O2PointApplyAffineTransform(v0.p,pathToSurface);
O2Point v1p=O2PointApplyAffineTransform(v1.p,pathToSurface);
O2Point n=O2PointApplyAffineTransformNoTranslate(Vector2MultiplyByFloat(Vector2Normalize(Vector2PerpendicularCCW(v1.t)) , strokeWidth * 0.5f),pathToSurface);
O2Point npccw = Vector2Add(v0p, n);
O2Point npcw = Vector2Subtract(v0p, n);
O2Point nnccw = Vector2Add(v1p,n);
O2Point nncw = Vector2Subtract(v1p , n);
O2DContextAddEdge(context,npccw, nnccw);
O2DContextAddEdge(context,nnccw, nncw);
O2DContextAddEdge(context,nncw, npcw);
O2DContextAddEdge(context,npcw, npccw);
#if 0
if(Vector2Dot(n,v0.t) <= 0.0f){
O2DContextAddEdge(context,pnccw, npcw);
O2DContextAddEdge(context,npcw, pncw);
O2DContextAddEdge(context,pncw, npccw);
O2DContextAddEdge(context,npccw, pnccw);
}
else {
O2DContextAddEdge(context,pnccw, npccw);
O2DContextAddEdge(context,npccw, pncw);
O2DContextAddEdge(context,pncw, npcw);
O2DContextAddEdge(context,npcw, pnccw);
}
ppccw = npccw;
ppcw = npcw;
pnccw = nnccw;
pncw = nncw;
//connect the last segment to the end coordinates
n = Vector2PerpendicularCCW(v1.t);
if(Vector2Dot(n,tangent) <= 0.0f){
O2DContextAddEdge(context,pnccw, endcw);
O2DContextAddEdge(context,endcw, pncw);
O2DContextAddEdge(context,pncw, endccw);
O2DContextAddEdge(context,endccw, pnccw);
}
else {
O2DContextAddEdge(context,pnccw, endccw);
O2DContextAddEdge(context,endccw, pncw);
O2DContextAddEdge(context,pncw, endcw);
O2DContextAddEdge(context,endcw, pnccw);
}
#endif
}
else {
O2Point prev = v0.p;
O2Point prevt = v0.t;
int j;
for(j=0;j<samples;j++){
O2Float t = (O2Float)(j+1) / (O2Float)samples;
O2Point position = Vector2Add(Vector2MultiplyByFloat(v0.p , (1.0f - t)) , Vector2MultiplyByFloat(v1.p ,t));
O2Point tangent = circularLerp(v0.t, v1.t, t);
O2Point n = Vector2MultiplyByFloat(Vector2Normalize(Vector2PerpendicularCCW(tangent)) , strokeWidth * 0.5f);
if(j == samples-1)
position = v1.p;
O2Point npccw = O2PointApplyAffineTransform(Vector2Add(prev, n),pathToSurface);
O2Point npcw = O2PointApplyAffineTransform(Vector2Subtract(prev, n),pathToSurface);
O2Point nnccw = O2PointApplyAffineTransform(Vector2Add(position,n),pathToSurface);
O2Point nncw = O2PointApplyAffineTransform(Vector2Subtract(position , n),pathToSurface);
O2DContextAddEdge(context,npccw, nnccw);
O2DContextAddEdge(context,nnccw, nncw);
O2DContextAddEdge(context,nncw, npcw);
O2DContextAddEdge(context,npcw, npccw);
if(Vector2Dot(n,prevt) <= 0.0f){
O2DContextAddEdge(context,pnccw, npcw);
O2DContextAddEdge(context,npcw, pncw);
O2DContextAddEdge(context,pncw, npccw);
O2DContextAddEdge(context,npccw, pnccw);
}
else {
O2DContextAddEdge(context,pnccw, npccw);
O2DContextAddEdge(context,npccw, pncw);
O2DContextAddEdge(context,pncw, npcw);
O2DContextAddEdge(context,npcw, pnccw);
}
ppccw = npccw;
ppcw = npcw;
pnccw = nnccw;
pncw = nncw;
prev = position;
prevt = tangent;
}
//connect the last segment to the end coordinates
O2Point n = Vector2PerpendicularCCW(v1.t);
if(Vector2Dot(n,prevt) <= 0.0f){
O2DContextAddEdge(context,pnccw, endcw);
O2DContextAddEdge(context,endcw, pncw);
O2DContextAddEdge(context,pncw, endccw);
O2DContextAddEdge(context,endccw, pnccw);
}
else {
O2DContextAddEdge(context,pnccw, endccw);
O2DContextAddEdge(context,endccw, pncw);
O2DContextAddEdge(context,pncw, endcw);
O2DContextAddEdge(context,endcw, pnccw);
}
}
}
// Generate edges for stroke caps. Resulting polygons are closed.
void VGPathDoCap(O2AffineTransform pathToSurface, O2Context_builtin *context,StrokeVertex v, O2Float strokeWidth, O2LineCap capStyle){
O2Point ccwt = O2PointApplyAffineTransform(v.ccw,pathToSurface);
O2Point cwt = O2PointApplyAffineTransform(v.cw,pathToSurface);
switch(capStyle){
case kO2LineCapButt:
break;
case kO2LineCapRound: {
const O2Float tessellationAngle = 5.0f;
O2Float angle = 180.0f / tessellationAngle;
int samples = (int)ceil(angle);
O2Float step = 1.0f / samples;
O2Float t = step;
O2Point u0 = Vector2Normalize(Vector2Subtract(v.ccw,v.p));
O2Point u1 = Vector2Normalize(Vector2Subtract(v.cw,v.p));
O2Point prev = ccwt;
O2DContextAddEdge(context,cwt, ccwt);
int j;
for(j=1;j<samples;j++){
#if 1
O2Point vp=O2PointApplyAffineTransform(v.p,pathToSurface);
O2Point next=O2PointApplyAffineTransformNoTranslate(Vector2MultiplyByFloat(circularLerpWithDirection(u0, u1, t) , strokeWidth * 0.5f),pathToSurface);
next=Vector2Add(vp,next);
#else
O2Point next = Vector2Add(v.p , Vector2MultiplyByFloat(circularLerpWithDirection(u0, u1, t) , strokeWidth * 0.5f));
next = O2PointApplyAffineTransform(next,pathToSurface);
#endif
O2DContextAddEdge(context,prev, next);
prev = next;
t += step;
}
O2DContextAddEdge(context,prev, cwt);
break;
}
case kO2LineCapSquare: {
O2Point t = v.t;
t=Vector2Normalize(t);
O2Point vccw=O2PointApplyAffineTransform(v.ccw,pathToSurface);
O2Point vcw=O2PointApplyAffineTransform(v.cw,pathToSurface);
O2Point strokeRadius=O2PointApplyAffineTransformNoTranslate(Vector2MultiplyByFloat(t , strokeWidth * 0.5f),pathToSurface);
O2Point ccws = Vector2Add(vccw , strokeRadius);
O2Point cws = Vector2Add(vcw , strokeRadius);
O2DContextAddEdge(context,cwt, ccwt);
O2DContextAddEdge(context,ccwt, ccws);
O2DContextAddEdge(context,ccws, cws);
O2DContextAddEdge(context,cws, cwt);
break;
}
}
}
// Generate edges for stroke joins. Resulting polygons are closed.
void VGPathDoJoin(O2AffineTransform pathToSurface, O2Context_builtin *context, StrokeVertex v0, StrokeVertex v1, O2Float strokeWidth, O2LineJoin joinStyle, O2Float miterLimit){
O2Point ccw0t = O2PointApplyAffineTransform(v0.ccw,pathToSurface);
O2Point cw0t = O2PointApplyAffineTransform(v0.cw,pathToSurface);
O2Point ccw1t = O2PointApplyAffineTransform(v1.ccw,pathToSurface);
O2Point cw1t = O2PointApplyAffineTransform(v1.cw,pathToSurface);
O2Point m0t = O2PointApplyAffineTransform(v0.p,pathToSurface);
O2Point m1t = O2PointApplyAffineTransform(v1.p,pathToSurface);
O2Point tccw = Vector2Subtract(v1.ccw,v0.ccw);
O2Point s, e, m, st, et;
BOOL cw;
if( Vector2Dot(tccw, v0.t) > 0.0f )
{ //draw ccw miter (draw from point 0 to 1)
s = ccw0t;
e = ccw1t;
st = v0.t;
et = v1.t;
m = ccw0t;
cw = NO;
O2DContextAddEdge(context,m0t, ccw0t);
O2DContextAddEdge(context,ccw1t, m1t);
O2DContextAddEdge(context,m1t, m0t);
}
else
{ //draw cw miter (draw from point 1 to 0)
s = cw1t;
e = cw0t;
st = v1.t;
et = v0.t;
m = cw0t;
cw = YES;
O2DContextAddEdge(context,cw0t, m0t);
O2DContextAddEdge(context,m1t, cw1t);
O2DContextAddEdge(context,m0t, m1t);
}
switch(joinStyle)
{
case kO2LineJoinMiter:
{
O2Float theta = (O2Float)acos(RI_CLAMP(Vector2Dot(v0.t, Vector2Negate(v1.t)), -1.0f, 1.0f));
O2Float miterLengthPerStrokeWidth = 1.0f / (O2Float)sin(theta*0.5f);
if( miterLengthPerStrokeWidth < miterLimit )
{ //miter
O2Float l = (O2Float)cos(theta*0.5f) * miterLengthPerStrokeWidth * (strokeWidth * 0.5f);
l = RI_MIN(l, RI_FLOAT_MAX); //force finite
O2Point c = Vector2Add(m , O2PointApplyAffineTransformNoTranslate(Vector2MultiplyByFloat(v0.t, l),pathToSurface));
O2DContextAddEdge(context,s, c);
O2DContextAddEdge(context,c, e);
break;
}
// bevel
// dropthrough
}
case kO2LineJoinBevel:
O2DContextAddEdge(context,s, e);
break;
case kO2LineJoinRound:
{
const O2Float tessellationAngle = 5.0f;
O2Point prev = s;
O2Float angle = RI_RAD_TO_DEG((O2Float)acos(RI_CLAMP(Vector2Dot(st, et), -1.0f, 1.0f))) / tessellationAngle;
int samples = (int)ceil(angle);
if( samples )
{
O2Float step = 1.0f / samples;
O2Float t = step;
int j;
for(j=1;j<samples;j++)
{
O2Point position = O2PointApplyAffineTransform(Vector2Add(Vector2MultiplyByFloat(v0.p , (1.0f - t)) , Vector2MultiplyByFloat(v1.p , t)),pathToSurface);
O2Point tangent = circularLerpWithDirection(st, et, t);
O2Point strokeRadius=O2PointApplyAffineTransformNoTranslate(Vector2MultiplyByFloat(Vector2Normalize(Vector2Perpendicular(tangent, cw)) , strokeWidth * 0.5f),pathToSurface);
O2Point next = Vector2Add(position , strokeRadius);
O2DContextAddEdge(context,prev, next);
prev = next;
t += step;
}
}
O2DContextAddEdge(context,prev, e);
break;
}
}
}
// Tessellate a path, apply stroking, dashing, caps and joins, and append resulting edges to a context.
void VGPathStroke(VGPath *self,O2AffineTransform pathToSurface, O2Context_builtin *context, const O2Float* dashPattern,int dashPatternSize, O2Float dashPhase, BOOL dashPhaseReset, O2Float strokeWidth, O2LineCap capStyle, O2LineJoin joinStyle, O2Float miterLimit){
RI_ASSERT(strokeWidth >= 0.0f);
RI_ASSERT(miterLimit >= 1.0f);
VGPathTessellateIfNeeded(self);
if(!self->_vertexCount)
return;
BOOL dashing = YES;
if( dashPatternSize & 1 )
dashPatternSize--; //odd number of dash pattern entries, discard the last one
O2Float dashPatternLength = 0.0f;
int i;
for(i=0;i<dashPatternSize;i++)
dashPatternLength += RI_MAX(dashPattern[i], 0.0f);
if(!dashPatternSize || dashPatternLength == 0.0f )
dashing = NO;
dashPatternLength = RI_MIN(dashPatternLength, RI_FLOAT_MAX);
//walk along the path
//stop at the next event which is either:
//-path vertex
//-dash stop
//for robustness, decisions based on geometry are done only once.
//inDash keeps track whether the last point was in dash or not
//loop vertex events
O2Float nextDash = 0.0f;
int d = 0;
BOOL inDash = YES;
StrokeVertex v0=StrokeVertexInit(), v1=StrokeVertexInit(), vs=StrokeVertexInit();
if(!dashing){
for(i=0;i<self->_vertexCount;i++){
const Vertex v = self->_vertices[i];
v1.p = v.userPosition;
v1.t = v.userTangent;
v1.ccw = Vector2Add(v1.p , Vector2MultiplyByFloat(Vector2Normalize(Vector2PerpendicularCCW(v1.t)) , strokeWidth * 0.5f));
v1.cw = Vector2Add(v1.p , Vector2MultiplyByFloat(Vector2Normalize(Vector2PerpendicularCW(v1.t)) , strokeWidth * 0.5f));
v1.pathLength = v.pathLength;
v1.flags = v.flags;
//process the vertex event
if(v.flags & START_SEGMENT) {
if(v.flags & START_SUBPATH)
vs = v1; //save the subpath start point
else {
if( v.flags & IMPLICIT_CLOSE_SUBPATH ) { //do caps for the start and end of the current subpath
VGPathDoCap(pathToSurface, context, v0, strokeWidth, capStyle); //end cap
StrokeVertex vi = vs;
vi.t = Vector2Negate(vi.t);
RI_SWAP(&vi.ccw.x, &vi.cw.x);
RI_SWAP(&vi.ccw.y, &vi.cw.y);
VGPathDoCap(pathToSurface, context, vi, strokeWidth, capStyle); //start cap
}
else { //join two segments
VGPathDoJoin(pathToSurface, context, v0, v1, strokeWidth, joinStyle, miterLimit);
}
}
}
else { //in the middle of a segment
if( !(v.flags & IMPLICIT_CLOSE_SUBPATH) ) { //normal segment, do stroking
VGPathInterpolateStroke(pathToSurface, context, v0, v1, strokeWidth);
}
}
if((v.flags & END_SEGMENT) && (v.flags & CLOSE_SUBPATH)) { //join start and end of the current subpath
VGPathDoJoin(pathToSurface, context, v1, vs, strokeWidth, joinStyle, miterLimit);
}
v0 = v1;
}
}
else {
for(i=0;i<self->_vertexCount;i++)
{
//read the next vertex
const Vertex v = self->_vertices[i];
v1.p = v.userPosition;
v1.t = v.userTangent;
RI_ASSERT(!Vector2IsZero(v1.t)); //don't allow zero tangents
v1.ccw = Vector2Add(v1.p , Vector2MultiplyByFloat(Vector2Normalize(Vector2PerpendicularCCW(v1.t)) , strokeWidth * 0.5f));
v1.cw = Vector2Add(v1.p , Vector2MultiplyByFloat(Vector2Normalize(Vector2PerpendicularCW(v1.t)) , strokeWidth * 0.5f));
v1.pathLength = v.pathLength;
v1.flags = v.flags;
v1.inDash = dashing ? inDash : YES; //NOTE: for other than START_SEGMENT vertices inDash will be updated after dashing
//process the vertex event
if(v.flags & START_SEGMENT)
{
if(v.flags & START_SUBPATH)
{
if( dashing )
{ //initialize dashing by finding which dash or gap the first point of the path lies in
if(dashPhaseReset || i == 0)
{
d = 0;
inDash = YES;
nextDash = v1.pathLength - RI_MOD(dashPhase, dashPatternLength);
for(;;)
{
O2Float prevDash = nextDash;
nextDash = prevDash + RI_MAX(dashPattern[d], 0.0f);
if(nextDash >= v1.pathLength)
break;
if( d & 1 )
inDash = YES;
else
inDash = NO;
d = (d+1) % dashPatternSize;
}
v1.inDash = inDash;
//the first point of the path lies between prevDash and nextDash
//d in the index of the next dash stop
//inDash is YES if the first point is in a dash
}
}
vs = v1; //save the subpath start point
}
else
{
if( v.flags & IMPLICIT_CLOSE_SUBPATH )
{ //do caps for the start and end of the current subpath
if( v0.inDash )
VGPathDoCap(pathToSurface, context, v0, strokeWidth, capStyle); //end cap
if( vs.inDash )
{
StrokeVertex vi = vs;
vi.t = Vector2Negate(vi.t);
RI_SWAP(&vi.ccw.x, &vi.cw.x);
RI_SWAP(&vi.ccw.y, &vi.cw.y);
VGPathDoCap(pathToSurface, context, vi, strokeWidth, capStyle); //start cap
}
}
else
{ //join two segments
RI_ASSERT(v0.inDash == v1.inDash);
if( v0.inDash )
VGPathDoJoin(pathToSurface, context, v0, v1, strokeWidth, joinStyle, miterLimit);
}
}
}
else
{ //in the middle of a segment
if( !(v.flags & IMPLICIT_CLOSE_SUBPATH) )
{ //normal segment, do stroking
if( dashing )
{
StrokeVertex prevDashVertex = v0; //dashing of the segment starts from the previous vertex
if(nextDash + 10000.0f * dashPatternLength < v1.pathLength)
NSLog(@"too many dashes");
//loop dash events until the next vertex event
//zero length dashes are handled as a special case since if they hit the vertex,
//we want to include their starting point to this segment already in order to generate a join
int numDashStops = 0;
while(nextDash < v1.pathLength || (nextDash <= v1.pathLength && dashPattern[(d+1) % dashPatternSize] == 0.0f))
{
O2Float edgeLength = v1.pathLength - v0.pathLength;
O2Float ratio = 0.0f;
if(edgeLength > 0.0f)
ratio = (nextDash - v0.pathLength) / edgeLength;
StrokeVertex nextDashVertex=StrokeVertexInit();
nextDashVertex.p = Vector2Add(Vector2MultiplyByFloat(v0.p , (1.0f - ratio)) , Vector2MultiplyByFloat(v1.p , ratio));
nextDashVertex.t = circularLerp(v0.t, v1.t, ratio);
nextDashVertex.ccw = Vector2Add(nextDashVertex.p , Vector2MultiplyByFloat(Vector2Normalize(Vector2PerpendicularCCW(nextDashVertex.t)) , strokeWidth * 0.5f));
nextDashVertex.cw = Vector2Add(nextDashVertex.p , Vector2MultiplyByFloat(Vector2Normalize(Vector2PerpendicularCW(nextDashVertex.t)) , strokeWidth * 0.5f));
if( inDash )
{ //stroke from prevDashVertex -> nextDashVertex
if( numDashStops )
{ //prevDashVertex is not the start vertex of the segment, cap it (start vertex has already been joined or capped)
StrokeVertex vi = prevDashVertex;
vi.t = Vector2Negate(vi.t);
RI_SWAP(&vi.ccw.x, &vi.cw.x);
RI_SWAP(&vi.ccw.y, &vi.cw.y);
VGPathDoCap(pathToSurface, context, vi, strokeWidth, capStyle);
}
VGPathInterpolateStroke(pathToSurface, context, prevDashVertex, nextDashVertex, strokeWidth);
VGPathDoCap(pathToSurface, context, nextDashVertex, strokeWidth, capStyle); //end cap
}
prevDashVertex = nextDashVertex;
if( d & 1 )
{ //dash starts
RI_ASSERT(!inDash);
inDash = YES;
}
else
{ //dash ends
RI_ASSERT(inDash);
inDash = NO;
}
d = (d+1) % dashPatternSize;
nextDash += RI_MAX(dashPattern[d], 0.0f);
numDashStops++;
}
if( inDash )
{ //stroke prevDashVertex -> v1
if( numDashStops )
{ //prevDashVertex is not the start vertex of the segment, cap it (start vertex has already been joined or capped)
StrokeVertex vi = prevDashVertex;
vi.t = Vector2Negate(vi.t);
RI_SWAP(&vi.ccw.x, &vi.cw.x);
RI_SWAP(&vi.ccw.y, &vi.cw.y);
VGPathDoCap(pathToSurface, context, vi, strokeWidth, capStyle);
}
VGPathInterpolateStroke(pathToSurface, context, prevDashVertex, v1, strokeWidth);
//no cap, leave path open
}
v1.inDash = inDash; //update inDash status of the segment end point
}
else //no dashing, just interpolate segment end points
VGPathInterpolateStroke(pathToSurface, context, v0, v1, strokeWidth);
}
}
if((v.flags & END_SEGMENT) && (v.flags & CLOSE_SUBPATH))
{ //join start and end of the current subpath
if( v1.inDash && vs.inDash )
VGPathDoJoin(pathToSurface, context, v1, vs, strokeWidth, joinStyle, miterLimit);
else
{ //both start and end are not in dash, cap them
if( v1.inDash )
VGPathDoCap(pathToSurface, context, v1, strokeWidth, capStyle); //end cap
if( vs.inDash )
{
StrokeVertex vi = vs;
vi.t = Vector2Negate(vi.t);
RI_SWAP(&vi.ccw.x, &vi.cw.x);
RI_SWAP(&vi.ccw.y, &vi.cw.y);
VGPathDoCap(pathToSurface, context, vi, strokeWidth, capStyle); //start cap
}
}
}
v0 = v1;
}
}
}
// Tessellates a path, and returns a position and a tangent on the path given a distance along the path.
void VGPathGetPointAlong(VGPath *self,int startIndex, int numSegments, O2Float distance, O2Point *p, O2Point *t){
RI_ASSERT(startIndex >= 0 && startIndex + numSegments <= self->_numberOfElements && numSegments > 0);
VGPathTessellateIfNeeded(self);
RI_ASSERT(startIndex >= 0 && startIndex < self->_numberOfElements);
RI_ASSERT(startIndex + numSegments >= 0 && startIndex + numSegments <= self->_numberOfElements);
int startVertex = self->_segmentToVertex[startIndex].start;
int endVertex = self->_segmentToVertex[startIndex + numSegments - 1].end;
if(!self->_vertexCount || (startVertex == -1 && endVertex == -1))
{ // no vertices in the tessellated path. The path is empty or consists only of zero-length segments.
*p=O2PointMake(0,0);
*t=O2PointMake(1,0);
return;
}
if(startVertex == -1)
startVertex = 0;
RI_ASSERT(startVertex >= 0 && startVertex < self->_vertexCount);
RI_ASSERT(endVertex >= 0 && endVertex < self->_vertexCount);
distance += self->_vertices[startVertex].pathLength; //map distance to the range of the whole path
if(distance <= self->_vertices[startVertex].pathLength)
{ //return the first point of the path
*p = self->_vertices[startVertex].userPosition;
*t = self->_vertices[startVertex].userTangent;
return;
}
if(distance >= self->_vertices[endVertex].pathLength)
{ //return the last point of the path
*p = self->_vertices[endVertex].userPosition;
*t = self->_vertices[endVertex].userTangent;
return;
}
//search for the segment containing the distance
int s;
for(s=startIndex;s<startIndex+numSegments;s++)
{
int start = self->_segmentToVertex[s].start;
int end = self->_segmentToVertex[s].end;
if(start < 0)
start = 0;
if(end < 0)
end = 0;
RI_ASSERT(start >= 0 && start < self->_vertexCount);
RI_ASSERT(end >= 0 && end < self->_vertexCount);
if(distance >= self->_vertices[start].pathLength && distance < self->_vertices[end].pathLength)
{ //segment contains the queried distance
int i;
for(i=start;i<end;i++)
{
Vertex v0 = self->_vertices[i];
Vertex v1 = self->_vertices[i+1];
if(distance >= v0.pathLength && distance < v1.pathLength)
{ //segment found, interpolate linearly between its end points
O2Float edgeLength = v1.pathLength - v0.pathLength;
RI_ASSERT(edgeLength > 0.0f);
O2Float r = (distance - v0.pathLength) / edgeLength;
*p = Vector2Add(Vector2MultiplyByFloat(v0.userPosition , (1.0f - r)) , Vector2MultiplyByFloat(v1.userPosition , r));
*t = Vector2Add(Vector2MultiplyByFloat(v0.userTangent,(1.0f - r)) , Vector2MultiplyByFloat(v1.userTangent,r));
return;
}
}
}
}
RI_ASSERT(0); //point not found (should never get here)
}
// Tessellates a path, and computes its length.
O2Float VGPathGetLength(VGPath *self,int startIndex, int numSegments){
RI_ASSERT(startIndex >= 0 && startIndex + numSegments <= self->_numberOfElements && numSegments > 0);
VGPathTessellateIfNeeded(self);
RI_ASSERT(startIndex >= 0 && startIndex < self->_numberOfElements);
RI_ASSERT(startIndex + numSegments >= 0 && startIndex + numSegments <= self->_numberOfElements);
int startVertex = self->_segmentToVertex[startIndex].start;
int endVertex = self->_segmentToVertex[startIndex + numSegments - 1].end;
if(!self->_vertexCount)
return 0.0f;
O2Float startPathLength = 0.0f;
if(startVertex >= 0)
{
RI_ASSERT(startVertex >= 0 && startVertex < self->_vertexCount);
startPathLength = self->_vertices[startVertex].pathLength;
}
O2Float endPathLength = 0.0f;
if(endVertex >= 0)
{
RI_ASSERT(endVertex >= 0 && endVertex < self->_vertexCount);
endPathLength = self->_vertices[endVertex].pathLength;
}
return endPathLength - startPathLength;
}
// Tessellates a path, and computes its bounding box in user space.
void VGPathGetPathBounds(VGPath *self,O2Float *minx, O2Float *miny, O2Float *maxx, O2Float *maxy){
VGPathTessellateIfNeeded(self);
if(self->_vertexCount)
{
*minx = self->m_userMinx;
*miny = self->m_userMiny;
*maxx = self->m_userMaxx;
*maxy = self->m_userMaxy;
}
else
{
*minx = *miny = 0;
*maxx = *maxy = -1;
}
}
// Tessellates a path, and computes its bounding box in surface space.
void VGPathGetPathTransformedBounds(VGPath *self,O2AffineTransform pathToSurface, O2Float *minx, O2Float *miny, O2Float *maxx, O2Float *maxy){
VGPathTessellateIfNeeded(self);
if(self->_vertexCount==0) {
*minx = *miny = 0;
*maxx = *maxy = -1;
}
else {
O2Point p0=O2PointMake(self->m_userMinx, self->m_userMiny);
O2Point p1=O2PointMake(self->m_userMinx, self->m_userMaxy);
O2Point p2=O2PointMake(self->m_userMaxx, self->m_userMaxy);
O2Point p3=O2PointMake(self->m_userMaxx, self->m_userMiny);
p0 = O2PointApplyAffineTransform(p0,pathToSurface);
p1 = O2PointApplyAffineTransform(p1,pathToSurface);
p2 = O2PointApplyAffineTransform(p2,pathToSurface);
p3 = O2PointApplyAffineTransform(p3,pathToSurface);
*minx = RI_MIN(RI_MIN(RI_MIN(p0.x, p1.x), p2.x), p3.x);
*miny = RI_MIN(RI_MIN(RI_MIN(p0.y, p1.y), p2.y), p3.y);
*maxx = RI_MAX(RI_MAX(RI_MAX(p0.x, p1.x), p2.x), p3.x);
*maxy = RI_MAX(RI_MAX(RI_MAX(p0.y, p1.y), p2.y), p3.y);
}
}
// Adds a vertex to a tessellated path.
void VGPathAddVertex(VGPath *self,O2Point p, O2Point t, O2Float pathLength, unsigned int flags){
RI_ASSERT(!Vector2IsZero(t));
Vertex v;
v.pathLength = pathLength;
v.userPosition = p;
v.userTangent = t;
v.flags = flags;
if(self->_vertexCount+1>self->_vertexCapacity){
self->_vertexCapacity*=2;
self->_vertices=(Vertex *)NSZoneRealloc(NULL,self->_vertices,self->_vertexCapacity*sizeof(Vertex));
}
self->_vertices[self->_vertexCount++]=v;
self->m_userMinx = RI_MIN(self->m_userMinx, v.userPosition.x);
self->m_userMiny = RI_MIN(self->m_userMiny, v.userPosition.y);
self->m_userMaxx = RI_MAX(self->m_userMaxx, v.userPosition.x);
self->m_userMaxy = RI_MAX(self->m_userMaxy, v.userPosition.y);
}
// Adds an edge to a tessellated path.
void VGPathAddEdge(VGPath *self,O2Point p0, O2Point p1, O2Point t0, O2Point t1, unsigned int startFlags, unsigned int endFlags){
O2Float pathLength = 0.0f;
RI_ASSERT(!Vector2IsZero(t0) && !Vector2IsZero(t1));
//segment midpoints are shared between edges
if( startFlags & START_SEGMENT )
{
if(self->_vertexCount > 0)
pathLength = self->_vertices[self->_vertexCount-1].pathLength;
VGPathAddVertex(self,p0, t0, pathLength, startFlags);
}
//other than implicit close paths (caused by a MOVE_TO) add to path length
if( !(endFlags & IMPLICIT_CLOSE_SUBPATH) )
{
//NOTE: with extremely large coordinates the floating point path length is infinite
O2Float l = Vector2Length(Vector2Subtract(p1,p0));
pathLength = self->_vertices[self->_vertexCount-1].pathLength + l;
pathLength = RI_MIN(pathLength, RI_FLOAT_MAX);
}
VGPathAddVertex(self,p1, t1, pathLength, endFlags);
}
// Tessellates a close-path segment.
void VGPathAddEndPath(VGPath *self,O2Point p0, O2Point p1, BOOL subpathHasGeometry, unsigned int flags){
if(!subpathHasGeometry)
{ //single vertex
O2Point t=O2PointMake(1.0f,0.0f);
VGPathAddEdge(self,p0, p1, t, t, START_SEGMENT | START_SUBPATH, END_SEGMENT | END_SUBPATH);
VGPathAddEdge(self,p0, p1, Vector2Negate(t), Vector2Negate(t), IMPLICIT_CLOSE_SUBPATH | START_SEGMENT, IMPLICIT_CLOSE_SUBPATH | END_SEGMENT);
return;
}
//the subpath contains segment commands that have generated geometry
//add a close path segment to the start point of the subpath
RI_ASSERT(self->_vertexCount > 0);
self->_vertices[self->_vertexCount-1].flags |= END_SUBPATH;
O2Point t = Vector2Normalize(Vector2Subtract(p1,p0));
if(Vector2IsZero(t))
t = self->_vertices[self->_vertexCount-1].userTangent; //if the segment is zero-length, use the tangent of the last segment end point so that proper join will be generated
RI_ASSERT(!Vector2IsZero(t));
VGPathAddEdge(self,p0, p1, t, t, flags | START_SEGMENT, flags | END_SEGMENT);
}
// Tessellates a line-to segment.
BOOL VGPathAddLineTo(VGPath *self,O2Point p0, O2Point p1, BOOL subpathHasGeometry){
if(Vector2IsEqual(p0 ,p1))
return NO; //discard zero-length segments
//compute end point tangents
O2Point t = Vector2Normalize(Vector2Subtract(p1,p0));
RI_ASSERT(!Vector2IsZero(t));
unsigned int startFlags = START_SEGMENT;
if(!subpathHasGeometry)
startFlags |= START_SUBPATH;
VGPathAddEdge(self,p0, p1, t, t, startFlags, END_SEGMENT);
return YES;
}
// Tessellates a quad-to segment.
/*
Given a quadratic B<>zier curve with control points (x0, y0), (x1, y1), and (x2, y2), an identical cubic B<>zier curve may be formed using the control points (x0, y0), (x0 + 2*x1, y0 + 2*y1)/3, (x2 + 2*x1, y2 + 2*y1)/3, (x2, y2)
*/
BOOL VGPathAddQuadTo(VGPath *self,O2Point p0, O2Point p1, O2Point p2, BOOL subpathHasGeometry){
if(Vector2IsEqual(p0,p1) && Vector2IsEqual(p0,p2))
{
RI_ASSERT(Vector2IsEqual(p1,p2));
return NO; //discard zero-length segments
}
//compute end point tangents
O2Point incomingTangent = Vector2Normalize(Vector2Subtract(p1,p0));
O2Point outgoingTangent = Vector2Normalize(Vector2Subtract(p2,p1));
if(Vector2IsEqual(p0,p1))
incomingTangent = Vector2Normalize(Vector2Subtract(p2,p0));
if(Vector2IsEqual(p1,p2))
outgoingTangent = Vector2Normalize(Vector2Subtract(p2 ,p0));
RI_ASSERT(!Vector2IsZero(incomingTangent) && !Vector2IsZero(outgoingTangent));
unsigned int startFlags = START_SEGMENT;
if(!subpathHasGeometry)
startFlags |= START_SUBPATH;
const int segments = 256;
O2Point pp = p0;
O2Point tp = incomingTangent;
unsigned int prevFlags = startFlags;
int i;
for(i=1;i<segments;i++)
{
O2Float t = (O2Float)i / (O2Float)segments;
O2Float u = 1.0f-t;
O2Point pn = Vector2Add(Vector2Add(Vector2MultiplyByFloat(p0,u*u) , Vector2MultiplyByFloat(p1,2.0f*t*u)),Vector2MultiplyByFloat(p2,t*t));
O2Point tn = Vector2Add(Vector2Add(Vector2MultiplyByFloat(p0,(-1.0f+t)), Vector2MultiplyByFloat(p1,(1.0f-2.0f*t))),Vector2MultiplyByFloat(p2,t));
tn = Vector2Normalize(tn);
if(Vector2IsZero(tn))
tn = tp;
VGPathAddEdge(self,pp, pn, tp, tn, prevFlags, 0);
pp = pn;
tp = tn;
prevFlags = 0;
}
VGPathAddEdge(self,pp, p2, tp, outgoingTangent, prevFlags, END_SEGMENT);
return YES;
}
// Tessellates a cubic-to segment.
#if 0
// Bezier to lines from: Windows Graphics Programming by Feng Yuan
static void bezier(VGPath *self,double x1,double y1,double x2, double y2,double x3,double y3,double x4,double y4,unsigned *prevFlags,O2Point *pp,O2Point *tp){
// Ax+By+C=0 is the line (x1,y1) (x4,y4);
double A=y4-y1;
double B=x1-x4;
double C=y1*(x4-x1)-x1*(y4-y1);
double AB=A*A+B*B;
if((A*x2+B*y2+C)*(A*x2+B*y2+C)<AB && (A*x3+B*y3+C)*(A*x3+B*y3+C)<AB){
O2Point v0=O2PointMake(x1,y1);
O2Point v1=O2PointMake(x4,y4);
O2Point t = Vector2Normalize(Vector2Subtract(v1,v0));
VGPathAddEdge(self,v0, v1, *tp, t, *prevFlags, 0);
*prevFlags=0;
*pp=v1;
*tp=t;
return;
}
else {
double x12=x1+x2;
double y12=y1+y2;
double x23=x2+x3;
double y23=y2+y3;
double x34=x3+x4;
double y34=y3+y4;
double x1223=x12+x23;
double y1223=y12+y23;
double x2334=x23+x34;
double y2334=y23+y34;
double x=x1223+x2334;
double y=y1223+y2334;
bezier(self,x1,y1,x12/2,y12/2,x1223/4,y1223/4,x/8,y/8,prevFlags,pp,tp);
bezier(self,x/8,y/8,x2334/4,y2334/4,x34/2,y34/2,x4,y4,prevFlags,pp,tp);
}
}
#endif
BOOL VGPathAddCubicTo(VGPath *self,O2Point p0, O2Point p1, O2Point p2, O2Point p3, BOOL subpathHasGeometry){
if(Vector2IsEqual(p0,p1) && Vector2IsEqual(p0,p2) && Vector2IsEqual(p0 ,p3))
{
RI_ASSERT(Vector2IsEqual(p1 , p2) && Vector2IsEqual(p1 , p3) && Vector2IsEqual(p2 , p3));
return NO; //discard zero-length segments
}
//compute end point tangents
O2Point incomingTangent = Vector2Normalize(Vector2Subtract(p1, p0));
O2Point outgoingTangent = Vector2Normalize(Vector2Subtract(p3, p2));
if(Vector2IsEqual(p0 , p1))
{
incomingTangent = Vector2Normalize(Vector2Subtract(p2 ,p0));
if(Vector2IsEqual(p1, p2))
incomingTangent = Vector2Normalize(Vector2Subtract(p3,p0));
}
if(Vector2IsEqual(p2, p3))
{
outgoingTangent = Vector2Normalize(Vector2Subtract(p3 ,p1));
if(Vector2IsEqual(p1, p2))
outgoingTangent = Vector2Normalize(Vector2Subtract(p3,p0));
}
RI_ASSERT(!Vector2IsZero(incomingTangent) && !Vector2IsZero(outgoingTangent));
unsigned int startFlags = START_SEGMENT;
if(!subpathHasGeometry)
startFlags |= START_SUBPATH;
#if 0
// This is the proper idea, subdivide until flatness tolerance is acheived
// However, it does not compensate for the CTM/device matrix, so it can produce grossly flat curves
// Also CRASHES under circumstances when a coordinate is NaN (view had NaN y)
unsigned int prevFlags = startFlags;
O2Point pp = p0;
O2Point tp = incomingTangent;
bezier(self,p0.x,p0.y,p1.x,p1.y,p2.x,p2.y,p3.x,p3.y,&prevFlags,&pp,&tp);
VGPathAddEdge(self,pp, p3, tp, outgoingTangent, prevFlags, END_SEGMENT);
#else
const int segments = 256;
O2Point pp = p0;
O2Point tp = incomingTangent;
unsigned int prevFlags = startFlags;
int i;
for(i=1;i<segments;i++)
{
O2Float t = (O2Float)i / (O2Float)segments;
O2Float u = 1.0f-t;
O2Point pn = Vector2Add(Vector2Add(Vector2Add(Vector2MultiplyByFloat(p0,u*u*u), Vector2MultiplyByFloat(p1,3.0f*t*u*u)) ,Vector2MultiplyByFloat(p2,3.0f*t*t*u)),Vector2MultiplyByFloat(p3,t*t*t));
O2Point tn = Vector2Add(Vector2Add(Vector2Add(Vector2MultiplyByFloat(p0,(-1.0f + 2.0f*t - t*t)) , Vector2MultiplyByFloat(p1,(1.0f - 4.0f*t + 3.0f*t*t))) , Vector2MultiplyByFloat(p2,(2.0f*t - 3.0f*t*t) )) ,Vector2MultiplyByFloat(p3,t*t));
tn = Vector2Normalize(tn);
if(Vector2IsZero(tn))
tn = tp;
VGPathAddEdge(self,pp, pn, tp, tn, prevFlags, 0);
pp = pn;
tp = tn;
prevFlags = 0;
}
VGPathAddEdge(self,pp, p3, tp, outgoingTangent, prevFlags, END_SEGMENT);
#endif
return YES;
}
// Tessellates a path.
/* tessellation output format: A list of vertices describing the
path tessellated into line segments and relevant aspects of the
input data. Each path segment has a start vertex, a number of
internal vertices (possibly zero), and an end vertex. The start
and end of segments and subpaths have been flagged, as well as
implicit and explicit close subpath segments. */
void VGPathTessellateIfNeeded(VGPath *self){
if( self->_vertexCount > 0 )
return; //already tessellated
self->m_userMinx = RI_FLOAT_MAX;
self->m_userMiny = RI_FLOAT_MAX;
self->m_userMaxx = -RI_FLOAT_MAX;
self->m_userMaxy = -RI_FLOAT_MAX;
{
unsigned numberOfElements=O2PathNumberOfElements(self->_path);
if(self->_segmentToVertexCapacity<numberOfElements){
self->_segmentToVertexCapacity=numberOfElements;
self->_segmentToVertex=NSZoneRealloc(NULL,self->_segmentToVertex,self->_segmentToVertexCapacity*sizeof(VertexIndex));
}
int coordIndex = 0;
O2Point s=O2PointMake(0,0); //the beginning of the current subpath
O2Point o=O2PointMake(0,0); //the last point of the previous segment
O2Point p=O2PointMake(0,0); //the last internal control point of the previous segment, if the segment was a (regular or smooth) quadratic or cubic Bezier, or else the last point of the previous segment
//tessellate the path segments
coordIndex = 0;
s=O2PointMake(0,0);
o=O2PointMake(0,0);
p=O2PointMake(0,0);
BOOL subpathHasGeometry = NO;
O2PathElementType prevSegment = kO2PathElementMoveToPoint;
int i;
const unsigned char *elements=O2PathElements(self->_path);
const O2Point *points=O2PathPoints(self->_path);
for(i=0;i<numberOfElements;i++)
{
O2PathElementType segment = elements[i];
int coords = O2PathElementTypeToNumCoordinates(segment);
self->_segmentToVertex[i].start = self->_vertexCount;
switch(segment)
{
case kO2PathElementCloseSubpath:
{
RI_ASSERT(coords == 0);
VGPathAddEndPath(self,o, s, subpathHasGeometry, CLOSE_SUBPATH);
p = s;
o = s;
subpathHasGeometry = NO;
break;
}
case kO2PathElementMoveToPoint:
{
RI_ASSERT(coords == 1);
O2Point c=points[coordIndex];
if(prevSegment != kO2PathElementMoveToPoint && prevSegment != kO2PathElementCloseSubpath)
VGPathAddEndPath(self,o, s, subpathHasGeometry, IMPLICIT_CLOSE_SUBPATH);
s = c;
p = c;
o = c;
subpathHasGeometry = NO;
break;
}
case kO2PathElementAddLineToPoint:
{
RI_ASSERT(coords == 1);
O2Point c=points[coordIndex];
if(VGPathAddLineTo(self,o, c, subpathHasGeometry))
subpathHasGeometry = YES;
p = c;
o = c;
break;
}
case kO2PathElementAddQuadCurveToPoint:
{
RI_ASSERT(coords == 2);
O2Point c0=points[coordIndex];
O2Point c1=points[coordIndex+1];
if(VGPathAddQuadTo(self,o, c0, c1, subpathHasGeometry))
subpathHasGeometry = YES;
p = c0;
o = c1;
break;
}
case kO2PathElementAddCurveToPoint:
{
RI_ASSERT(coords == 3);
O2Point c0=points[coordIndex+0];
O2Point c1=points[coordIndex+1];
O2Point c2=points[coordIndex+2];
if(VGPathAddCubicTo(self,o, c0, c1, c2, subpathHasGeometry))
subpathHasGeometry = YES;
p = c1;
o = c2;
break;
}
}
if(self->_vertexCount > self->_segmentToVertex[i].start)
{ //segment produced vertices
self->_segmentToVertex[i].end = self->_vertexCount - 1;
}
else
{ //segment didn't produce vertices (zero-length segment). Ignore it.
self->_segmentToVertex[i].start = self->_segmentToVertex[i].end = self->_vertexCount-1;
}
prevSegment = segment;
coordIndex += coords;
}
//add an implicit MOVE_TO to the end to close the last subpath.
//if the subpath contained only zero-length segments, this produces the necessary geometry to get it stroked
// and included in path bounds. The geometry won't be included in the pointAlongPath query.
if(prevSegment != kO2PathElementMoveToPoint && prevSegment != kO2PathElementCloseSubpath)
VGPathAddEndPath(self,o, s, subpathHasGeometry, IMPLICIT_CLOSE_SUBPATH);
#if 0 // DEBUG
//check that the flags are correct
int prev = -1;
BOOL subpathStarted = NO;
BOOL segmentStarted = NO;
for(int i=0;i<self->_vertexCount;i++)
{
Vertex v = self->_vertices[i];
if(v.flags & START_SUBPATH)
{
RI_ASSERT(!subpathStarted);
RI_ASSERT(v.flags & START_SEGMENT);
RI_ASSERT(!(v.flags & END_SUBPATH));
RI_ASSERT(!(v.flags & END_SEGMENT));
RI_ASSERT(!(v.flags & CLOSE_SUBPATH));
RI_ASSERT(!(v.flags & IMPLICIT_CLOSE_SUBPATH));
subpathStarted = YES;
}
if(v.flags & START_SEGMENT)
{
RI_ASSERT(subpathStarted || (v.flags & CLOSE_SUBPATH) || (v.flags & IMPLICIT_CLOSE_SUBPATH));
RI_ASSERT(!segmentStarted);
RI_ASSERT(!(v.flags & END_SUBPATH));
RI_ASSERT(!(v.flags & END_SEGMENT));
segmentStarted = YES;
}
if( v.flags & CLOSE_SUBPATH )
{
RI_ASSERT(segmentStarted);
RI_ASSERT(!subpathStarted);
RI_ASSERT((v.flags & START_SEGMENT) || (v.flags & END_SEGMENT));
RI_ASSERT(!(v.flags & IMPLICIT_CLOSE_SUBPATH));
RI_ASSERT(!(v.flags & START_SUBPATH));
RI_ASSERT(!(v.flags & END_SUBPATH));
}
if( v.flags & IMPLICIT_CLOSE_SUBPATH )
{
RI_ASSERT(segmentStarted);
RI_ASSERT(!subpathStarted);
RI_ASSERT((v.flags & START_SEGMENT) || (v.flags & END_SEGMENT));
RI_ASSERT(!(v.flags & CLOSE_SUBPATH));
RI_ASSERT(!(v.flags & START_SUBPATH));
RI_ASSERT(!(v.flags & END_SUBPATH));
}
if( prev >= 0 )
{
RI_ASSERT(segmentStarted);
RI_ASSERT(subpathStarted || ((self->_vertices[prev].flags & CLOSE_SUBPATH) && (self->_vertices[i].flags & CLOSE_SUBPATH)) ||
((self->_vertices[prev].flags & IMPLICIT_CLOSE_SUBPATH) && (self->_vertices[i].flags & IMPLICIT_CLOSE_SUBPATH)));
}
prev = i;
if(v.flags & END_SEGMENT)
{
RI_ASSERT(subpathStarted || (v.flags & CLOSE_SUBPATH) || (v.flags & IMPLICIT_CLOSE_SUBPATH));
RI_ASSERT(segmentStarted);
RI_ASSERT(!(v.flags & START_SUBPATH));
RI_ASSERT(!(v.flags & START_SEGMENT));
segmentStarted = NO;
prev = -1;
}
if(v.flags & END_SUBPATH)
{
RI_ASSERT(subpathStarted);
RI_ASSERT(v.flags & END_SEGMENT);
RI_ASSERT(!(v.flags & START_SUBPATH));
RI_ASSERT(!(v.flags & START_SEGMENT));
RI_ASSERT(!(v.flags & CLOSE_SUBPATH));
RI_ASSERT(!(v.flags & IMPLICIT_CLOSE_SUBPATH));
subpathStarted = NO;
}
}
#endif //RI_DEBUG
}
}
@end
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