= Transversal intersection of two parametric surfaces
{title2=$F(w)=S_1(u_1,v_1)-S_2(u_2,v_2)=0$}
At regular transverse intersections, the displayed map has a rank-three $3\times4$ <Jacobian matrix>. Its one-dimensional kernel is the parameter tangent, while the physical tangent is parallel to the <cross product> of the surface normals. A <continuation method> predicts along that tangent and corrects $F=0$ together with a transverse section equation using <Newton method>. Patch bounds and component isolation supply seeds; one seed alone cannot discover every disconnected curve or closed loop. Tangency or coincident surfaces violate the regular-curve assumptions and require separate analysis.
Back to article page
