A+B+C+D=0 from vector + dist

[Baker]

How can I get the A+B+C+D=0 plane formula from a Quake mplane_t normal and dist?

I am assuming the mplane_t normal vectors are perpendicular to the plane as one would expect.

[Barnes]

A+B+C= -D ?

[Spike]

its best expressed as A*x + B*y + C*z - D = 0

some useful formulas:
distfromplane = DotProduct (plane->normal, point) - plane->dist;
plane->dist = DotProduct(plane->normal, pointonplane);
pointonplane = point - (distfromplane*plane->normal);
isinfront = distfromplane>0;
isbehind = distfromplane<0;
isfloatingpointprecisionmiraclethatyouhavetosomehowrollintoonesideyetstillallowsplayerstofallthroughcracks = distfromplane==0;

note that the distance is negated relative to more standard plane notation. in mathematics, the plane is generally two-sided. in quake, the normal faces directly forwards into empty space (unless the surface has SURF_PLANEBACK set, in which case the normal faces backwards - all 4 values are logically negated (or in the case of nodes, the two children are pre-swapped, avoiding the need for the engine to do anything special). note that the plane normals in a quake bsp are arranged to be primarily positive, reducing the total number of planes needed, and facilitating axial lookups).
for surfaces, the two tangents are normally available via the texture vector values, but note that these vectors are not kept strictly perpedicular to the normal, nor are they always normalized. because quake is weird and has annoying texture mapping, as well as texture scaling.

[Baker]

[Spike]

the problem with drawing a plane is that a plane is infinitely long.

if you make a guess at a tangent (rotate the axis or just hardcode something), you can crossproduct it with the normal and normalize for a real tangent. and then do it again for some bitangent too. of course, these vectors have no relation to any texturing, but hey...
then you can generate a quad by moving '0 0 0' along the plane's normal onto the plane then extend sideways to find your four points.

alternatively you can figure out which axis is the most significant for the plane, pick a set of 4 points aligned on that axis, and then push them to match the plane.

if you're drawing a brush, once you have a quad you can then clip that quad by the other planes (retaining only the stuff on the inside of the brush). the resulting clipped polygon is your brush's face.

[Baker]

Just want to say thanks to Spike for help with these kinds of things over the years.

I did some plane/point tests today and this reminded me of how I struggled with this kind of thing in the past.

[toneddu2000]

[Baker]

[toneddu2000]