Plane3Plane3 intersection algebraic mistake

[Greezzee]

Plane specification formula is $Ax + By + Cz + D = 0$ Written using normals is $Dot(\vec{r}, \vec{N}) + D = 0$ So, in this function $Dot(\vec{N_0}, \vec{L}(t)) = -D_0$ and $Dot(\vec{N_1}, \vec{L}(t)) = -D_1$, so minus is missing

[davideberly]

Please read the comments immediately after the pragma-once statement in Hyperplane.h. My implementation of a plane with unit-length normal U and origin P is Dot(U,X-P) = 0. In terms of a plane constant c rather than specifying a plane origin, the equation is Dot(U,X) = c, where c = Dot(U,P). If U = (A,B,C) and X=(x,y,z), my plane is Ax+By+C*z-c = 0.

I believe my plane-plane intersection code is correct. For example,

    Plane3<double> plane0({ 0.0, 0.0, 1.0 }, 1.0);  // z = 1
    Plane3<double> plane1({ 0.0, 1.0, 0.0 }, -1.0);  // y = -1
    FIQuery<double, Plane3<double>, Plane3<double>> query{};
    auto result = query(plane0, plane1);
    // result.intersect = true
    // result.isLine = true
    // result.line.origin = (0, -1, 1) 
    // result.line.direction = (-1, 0, 0)
    // result.plane = <invalid, all members are zero>
    // NOTE: Points on the line of intersection have y = -1 and z = +1.

    // If I negate the right-hand sides of c0 and c1 as you suggest,
    // the line of intersection has points with y = +1 and z = -1,
    // but these are not my planes.
    double dot = Dot(plane0.normal, plane1.normal);
    double invDet = (double)1 / ((double)1 - dot * dot);
    double c0 = -(plane0.constant - dot * plane1.constant) * invDet;
    double c1 = -(plane1.constant - dot * plane0.constant) * invDet;
    result.intersect = true;
    result.isLine = true;
    result.line.origin = c0 * plane0.normal + c1 * plane1.normal;
    result.line.direction = UnitCross(plane0.normal, plane1.normal);
    // result.intersect = true
    // result.isLine = true
    // result.line.origin = (0, 1, -1)
    // result.line.direction = (-1, 0, 0)
    // result.plane = <invalid, all members are zero>