How to cut a surface at the intersection with another surface in Asymptote?

Question

In the code below, I define a cylinder (as a surface of revolution) and a plane (as a cyclic path). From both, I can get a surface that renders in 3D. Now, I would like to hide (or better remove) the part of the cylinder, which is below the surface (in this example at z < 0, rendered in a darker shade of red), while the plane should remain semi-transparent.

How can this be done elegantly?

import three;
import solids;

currentprojection = obliqueY();

path3 xyplane = path3(scale(10) * box((-1,-1),(1,1)));
revolution c =  rotate(-45,Y) * shift((0,0,-5)) *cylinder(O,1,15);

draw(surface(xyplane),black+opacity(.5));
draw(xyplane,black+linewidth(.1));

draw(surface(c),red);
draw(c,red);

Answer 1

Here's the workaround I came up with for this particular example. If the surface, you want to cut is a surface of revolution, you can define it as a parametric surface excluding the part below the plane. However, this is not a generic answer to the question.

import three;
import solids;

currentprojection = obliqueY();

path3 xyplane = path3(scale(10) * box((-1,-1),(1,1)));

surface cylinderSurfaceTiltedPlane(real R, real z0, real planeAlpha, real planePhi) {
    triple parametricCylinder(pair p) {
        real Phi = p.x;
        real Z = p.y;
        real x = R*sin(Phi);
        real y = R*cos(Phi);
        real z = Z * (tan(planeAlpha*pi/180)*sin(Phi - planePhi*pi/180)*R + z0)/z0;
        return (x,y,z);
    }
    return surface(parametricCylinder, (0,0), (2pi,z0), Spline);
}


draw(surface(xyplane),black+opacity(.5));
draw(xyplane,black+linewidth(.1));

surface cF = rotate(180-45,Y)  * shift((0,0,-10)) *     cylinderSurfaceTiltedPlane(1, 10, -45, 0);
draw(cF,red);