/** Calculate line boundary points.
*
* Sketch:
*
* uh1___uh2
* .' '.
* .' q '.
* .' ' ' '.
*.' ' .'. ' '.
* ' .' ul'. '
* p .' '. r
*
*
* ul can be found as above, uh1 and uh2 are much simpler:
*
* uh1 = q + ns * w/2, uh2 = q + nt * w/2
*/
func (polyline *polyLine) renderBevelEdge(sleeve, current, next mgl32.Vec2) {
t := next.Sub(current)
len_t := t.Len()
det := determinant(sleeve, t)
if mgl32.Abs(det)/(sleeve.Len()*len_t) < LINES_PARALLEL_EPS && sleeve.Dot(t) > 0 {
// lines parallel, compute as u1 = q + ns * w/2, u2 = q - ns * w/2
n := getNormal(t, polyline.halfwidth/len_t)
polyline.normals = append(polyline.normals, n)
polyline.normals = append(polyline.normals, n.Mul(-1))
polyline.generateEdges(current, 2)
return // early out
}
// cramers rule
sleeve_normal := getNormal(sleeve, polyline.halfwidth/sleeve.Len())
nt := getNormal(t, polyline.halfwidth/len_t)
lambda := determinant(nt.Sub(sleeve_normal), t) / det
d := sleeve_normal.Add(sleeve.Mul(lambda))
if det > 0 { // 'left' turn -> intersection on the top
polyline.normals = append(polyline.normals, d)
polyline.normals = append(polyline.normals, sleeve_normal.Mul(-1))
polyline.normals = append(polyline.normals, d)
polyline.normals = append(polyline.normals, nt.Mul(-1))
} else {
polyline.normals = append(polyline.normals, sleeve_normal)
polyline.normals = append(polyline.normals, d.Mul(-1))
polyline.normals = append(polyline.normals, nt)
polyline.normals = append(polyline.normals, d.Mul(-1))
}
polyline.generateEdges(current, 4)
}
/** Calculate line boundary points.
*
* Sketch:
*
* u1
* -------------+---...___
* | ```'''-- ---
* p- - - - - - q- - . _ _ | w/2
* | ` ' ' r +
* -------------+---...___ | w/2
* u2 ```'''-- ---
*
* u1 and u2 depend on four things:
* - the half line width w/2
* - the previous line vertex p
* - the current line vertex q
* - the next line vertex r
*
* u1/u2 are the intersection points of the parallel lines to p-q and q-r,
* i.e. the point where
*
* (q + w/2 * ns) + lambda * (q - p) = (q + w/2 * nt) + mu * (r - q) (u1)
* (q - w/2 * ns) + lambda * (q - p) = (q - w/2 * nt) + mu * (r - q) (u2)
*
* with nt,nt being the normals on the segments s = p-q and t = q-r,
*
* ns = perp(s) / |s|
* nt = perp(t) / |t|.
*
* Using the linear equation system (similar for u2)
*
* q + w/2 * ns + lambda * s - (q + w/2 * nt + mu * t) = 0 (u1)
* <=> q-q + lambda * s - mu * t = (nt - ns) * w/2
* <=> lambda * s - mu * t = (nt - ns) * w/2
*
* the intersection points can be efficiently calculated using Cramer's rule.
*/
func (polyline *polyLine) renderMiterEdge(sleeve, current, next mgl32.Vec2) {
sleeve_normal := getNormal(sleeve, polyline.halfwidth/sleeve.Len())
t := next.Sub(current)
len_t := t.Len()
det := determinant(sleeve, t)
// lines parallel, compute as u1 = q + ns * w/2, u2 = q - ns * w/2
if mgl32.Abs(det)/(sleeve.Len()*len_t) < LINES_PARALLEL_EPS && sleeve.Dot(t) > 0 {
polyline.normals = append(polyline.normals, sleeve_normal)
polyline.normals = append(polyline.normals, sleeve_normal.Mul(-1))
} else {
// cramers rule
nt := getNormal(t, polyline.halfwidth/len_t)
lambda := determinant(nt.Sub(sleeve_normal), t) / det
d := sleeve_normal.Add(sleeve.Mul(lambda))
polyline.normals = append(polyline.normals, d)
polyline.normals = append(polyline.normals, d.Mul(-1))
}
polyline.generateEdges(current, 2)
}