For 3 control point Bezier curves I would:
- use triangles as primitives
- enlarge control points to include area around curve to avoid artifacts
This way is fast and there is no problem to compute A',B',C'
from A,B,C
and vice versa. If the scale is constant (for example scale=1.25
) then the max usable curve thickness<=2.0*min(|control_point-M|)*(scale-1.0)
.
For safer enlargement you can compute exact scale needed (for example in geometry shader) and pass it to vertex and fragment … All of above can be done by Geometry shader. You should use transparency to correctly join the curves together. The average middle point should stay the same M=A+B+C=A'+B'+C'
if transparency is not an option
Then you need to change the approach so pass control points and position inside textures.
- create one 2D
float
texture with control points
- something like
float pnt[9][N]
pnt[0,1,2][]
is control pointA(x,y,z)
pnt[3,4,5][]
is control pointB(x,y,z)
pnt[6,7,8][]
is control pointC(x,y,z)
- also create 1D color texture
- something like
rgba col[N]
- The
x
axis resolution of both textures =N
is the number of Bezier curves
- now draw single Quad covering entire screen
And inside fragment shader check if pixel is inside any of the curve. If yes output its color …
This can get very slow for high Bezier curve count N
[edit1] almost collinear control points
for those I would use Quads
D,E
are mirrored pointsA,B
aroundC
D=C+C-A
E=C+C-B
C
is the middle pointM = (A+B+D+E)/4 = C = (A'+B'+C'+D')/4
- and
A',B',C',D'
are enlargedA,B,D,E
control points A'=C+(A -C)*scale
B'=C+(B -C)*scale
A =C+(A'-C)/scale
B =C+(B'-C)/scale
This can be used for any Bezier not just almost colinear but it uses larger polygons so it will be slower on performance (more fragments then really needed)
Here more advanced/optimized GLSL approach with complete implementation of cubic BEZIER curves: