多边形轮廓上的边缘并不总是正确的 [英] Edges on polygon outlines not always correct
本文介绍了多边形轮廓上的边缘并不总是正确的的处理方法，对大家解决问题具有一定的参考价值，需要的朋友们下面随着小编来一起学习吧！
问题描述
我使用下面的算法来生成四边形，然后渲染成这样的轮廓
<块引用>I'm using the algorithm below to generate quads which are then rendered to make an outline like this
The problem as seen on the image is that sometimes the lines are too thin when they should always be the same width. My algorithm finds the 4 vertices for the first one then the top 2 vertices of the next ones are the bottom 2 of the previous. This creates connected lines, but it seems to not always work. How could I fix this?
This is my algorithm:
void OGLENGINEFUNCTIONS::GenerateLinePoly(const std::vector<std::vector<GLdouble>> &input,
std::vector<GLfloat> &output, int width)
{
output.clear();
if(input.size() < 2)
{
return;
}
int temp;
float dirlen;
float perplen;
POINTFLOAT start;
POINTFLOAT end;
POINTFLOAT dir;
POINTFLOAT ndir;
POINTFLOAT perp;
POINTFLOAT nperp;
POINTFLOAT perpoffset;
POINTFLOAT diroffset;
POINTFLOAT p0, p1, p2, p3;
for(unsigned int i = 0; i < input.size() - 1; ++i)
{
start.x = static_cast<float>(input[i][0]);
start.y = static_cast<float>(input[i][1]);
end.x = static_cast<float>(input[i + 1][0]);
end.y = static_cast<float>(input[i + 1][1]);
dir.x = end.x - start.x;
dir.y = end.y - start.y;
dirlen = sqrt((dir.x * dir.x) + (dir.y * dir.y));
ndir.x = static_cast<float>(dir.x * 1.0 / dirlen);
ndir.y = static_cast<float>(dir.y * 1.0 / dirlen);
perp.x = dir.y;
perp.y = -dir.x;
perplen = sqrt((perp.x * perp.x) + (perp.y * perp.y));
nperp.x = static_cast<float>(perp.x * 1.0 / perplen);
nperp.y = static_cast<float>(perp.y * 1.0 / perplen);
perpoffset.x = static_cast<float>(nperp.x * width * 0.5);
perpoffset.y = static_cast<float>(nperp.y * width * 0.5);
diroffset.x = static_cast<float>(ndir.x * 0 * 0.5);
diroffset.y = static_cast<float>(ndir.y * 0 * 0.5);
// p0 = start + perpoffset - diroffset
// p1 = start - perpoffset - diroffset
// p2 = end + perpoffset + diroffset
// p3 = end - perpoffset + diroffset
p0.x = start.x + perpoffset.x - diroffset.x;
p0.y = start.y + perpoffset.y - diroffset.y;
p1.x = start.x - perpoffset.x - diroffset.x;
p1.y = start.y - perpoffset.y - diroffset.y;
if(i > 0)
{
temp = (8 * (i - 1));
p2.x = output[temp + 2];
p2.y = output[temp + 3];
p3.x = output[temp + 4];
p3.y = output[temp + 5];
}
else
{
p2.x = end.x + perpoffset.x + diroffset.x;
p2.y = end.y + perpoffset.y + diroffset.y;
p3.x = end.x - perpoffset.x + diroffset.x;
p3.y = end.y - perpoffset.y + diroffset.y;
}
output.push_back(p2.x);
output.push_back(p2.y);
output.push_back(p0.x);
output.push_back(p0.y);
output.push_back(p1.x);
output.push_back(p1.y);
output.push_back(p3.x);
output.push_back(p3.y);
}
}
Edit:
POINTFLOAT multiply(const POINTFLOAT &a, float b)
{
POINTFLOAT result;
result.x = a.x * b;
result.y = a.y * b;
return result;
}
POINTFLOAT normalize(const POINTFLOAT &a)
{
return multiply(a, 1.0f / sqrt(a.x * a.x + a.y * a.y));
}
POINTFLOAT slerp2d( const POINTFLOAT v0,
const POINTFLOAT v1, float t )
{
float dot = (v0.x * v1.x + v1.y * v1.y);
if( dot < -1.0f ) dot = -1.0f;
if( dot > 1.0f ) dot = 1.0f;
float theta_0 = acos( dot );
float theta = theta_0 * t;
POINTFLOAT v2;
v2.x = -v0.y;
v2.y = v0.x;
POINTFLOAT result;
result.x = v0.x * cos(theta) + v2.x * sin(theta);
result.y = v0.y * cos(theta) + v2.y * sin(theta);
return result;
}
void OGLENGINEFUNCTIONS::GenerateLinePoly(const std::vector<std::vector<GLdouble> > &input,
std::vector<GLfloat> &output, int width)
{
output.clear();
if(input.size() < 2)
{
return;
}
float w = width / 2.0f;
//glBegin(GL_TRIANGLES);
for( size_t i = 0; i < input.size()-1; ++i )
{
POINTFLOAT cur;
cur.x = input[i][0];
cur.y = input[i][1];
POINTFLOAT nxt;
nxt.x = input[i+1][0];
nxt.y = input[i+1][1];
POINTFLOAT b;
b.x = nxt.x - cur.x;
b.y = nxt.y - cur.y;
b = normalize(b);
POINTFLOAT b_perp;
b_perp.x = -b.y;
b_perp.y = b.x;
POINTFLOAT p0;
POINTFLOAT p1;
POINTFLOAT p2;
POINTFLOAT p3;
p0.x = cur.x + b_perp.x * w;
p0.y = cur.y + b_perp.y * w;
p1.x = cur.x - b_perp.x * w;
p1.y = cur.y - b_perp.y * w;
p2.x = nxt.x + b_perp.x * w;
p2.y = nxt.y + b_perp.y * w;
p3.x = nxt.x - b_perp.x * w;
p3.y = nxt.y - b_perp.y * w;
output.push_back(p0.x);
output.push_back(p0.y);
output.push_back(p1.x);
output.push_back(p1.y);
output.push_back(p2.x);
output.push_back(p2.y);
output.push_back(p2.x);
output.push_back(p2.y);
output.push_back(p1.x);
output.push_back(p1.y);
output.push_back(p3.x);
output.push_back(p3.y);
// only do joins when we have a prv
if( i == 0 ) continue;
POINTFLOAT prv;
prv.x = input[i-1][0];
prv.y = input[i-1][1];
POINTFLOAT a;
a.x = prv.x - cur.x;
a.y = prv.y - cur.y;
a = normalize(a);
POINTFLOAT a_perp;
a_perp.x = a.y;
a_perp.y = -a.x;
float det = a.x * b.y - b.x * a.y;
if( det > 0 )
{
a_perp.x = -a_perp.x;
a_perp.y = -a_perp.y;
b_perp.x = -b_perp.x;
b_perp.y = -b_perp.y;
}
// TODO: do inner miter calculation
// flip around normals and calculate round join points
a_perp.x = -a_perp.x;
a_perp.y = -a_perp.y;
b_perp.x = -b_perp.x;
b_perp.y = -b_perp.y;
size_t num_pts = 4;
std::vector< POINTFLOAT> round( 1 + num_pts + 1 );
POINTFLOAT nc;
nc.x = cur.x + (a_perp.x * w);
nc.y = cur.y + (a_perp.y * w);
round.front() = nc;
nc.x = cur.x + (b_perp.x * w);
nc.y = cur.y + (b_perp.y * w);
round.back() = nc;
for( size_t j = 1; j < num_pts+1; ++j )
{
float t = (float)j / (float)(num_pts + 1);
if( det > 0 )
{
POINTFLOAT nin;
nin = slerp2d( b_perp, a_perp, 1.0f-t );
nin.x *= w;
nin.y *= w;
nin.x += cur.x;
nin.y += cur.y;
round[j] = nin;
}
else
{
POINTFLOAT nin;
nin = slerp2d( a_perp, b_perp, t );
nin.x *= w;
nin.y *= w;
nin.x += cur.x;
nin.y += cur.y;
round[j] = nin;
}
}
for( size_t j = 0; j < round.size()-1; ++j )
{
output.push_back(cur.x);
output.push_back(cur.y);
if( det > 0 )
{
output.push_back(round[j + 1].x);
output.push_back(round[j + 1].y);
output.push_back(round[j].x);
output.push_back(round[j].y);
}
else
{
output.push_back(round[j].x);
output.push_back(round[j].y);
output.push_back(round[j + 1].x);
output.push_back(round[j + 1].y);
}
}
}
}
解决方案
Requires Eigen as written, but the core operations should map easily to whatever vector class you're using.
// v0 and v1 are normalized
// t can vary between 0 and 1
// http://number-none.com/product/Understanding%20Slerp,%20Then%20Not%20Using%20It/
Vector2f slerp2d( const Vector2f& v0, const Vector2f& v1, float t )
{
float dot = v0.dot(v1);
if( dot < -1.0f ) dot = -1.0f;
if( dot > 1.0f ) dot = 1.0f;
float theta_0 = acos( dot );
float theta = theta_0 * t;
Vector2f v2( -v0.y(), v0.x() );
return ( v0*cos(theta) + v2*sin(theta) );
}
void glPolyline( const vector<Vector2f>& polyline, float width )
{
if( polyline.size() < 2 ) return;
float w = width / 2.0f;
glBegin(GL_TRIANGLES);
for( size_t i = 0; i < polyline.size()-1; ++i )
{
const Vector2f& cur = polyline[ i ];
const Vector2f& nxt = polyline[i+1];
Vector2f b = (nxt - cur).normalized();
Vector2f b_perp( -b.y(), b.x() );
Vector2f p0( cur + b_perp*w );
Vector2f p1( cur - b_perp*w );
Vector2f p2( nxt + b_perp*w );
Vector2f p3( nxt - b_perp*w );
// first triangle
glVertex2fv( p0.data() );
glVertex2fv( p1.data() );
glVertex2fv( p2.data() );
// second triangle
glVertex2fv( p2.data() );
glVertex2fv( p1.data() );
glVertex2fv( p3.data() );
// only do joins when we have a prv
if( i == 0 ) continue;
const Vector2f& prv = polyline[i-1];
Vector2f a = (prv - cur).normalized();
Vector2f a_perp( a.y(), -a.x() );
float det = a.x()*b.y() - b.x()*a.y();
if( det > 0 )
{
a_perp = -a_perp;
b_perp = -b_perp;
}
// TODO: do inner miter calculation
// flip around normals and calculate round join points
a_perp = -a_perp;
b_perp = -b_perp;
size_t num_pts = 4;
vector< Vector2f > round( 1 + num_pts + 1 );
for( size_t j = 0; j <= num_pts+1; ++j )
{
float t = (float)j/(float)(num_pts+1);
if( det > 0 )
round[j] = cur + (slerp2d( b_perp, a_perp, 1.0f-t ) * w);
else
round[j] = cur + (slerp2d( a_perp, b_perp, t ) * w);
}
for( size_t j = 0; j < round.size()-1; ++j )
{
glVertex2fv( cur.data() );
if( det > 0 )
{
glVertex2fv( round[j+1].data() );
glVertex2fv( round[j+0].data() );
}
else
{
glVertex2fv( round[j+0].data() );
glVertex2fv( round[j+1].data() );
}
}
}
glEnd();
}
EDIT: Screenshots:
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