Draw arbitrary plane from plane equation, OpenGL

Question

I have a plane defined by the standard plane equation a*x + b*y + c*z + d = 0, which I would like to be able to draw using OpenGL. How can I derive the four points needed to draw it as a quadrilateral in 3D space? My plane type is defined as: ``` struct Plane { float x,y,z; // plane normal float d; }; void DrawPlane(const Plane & p) { ??? } ``` EDIT: So, rethinking the question, what I actually wanted was to draw a discreet representation of a plane in 3D space, not an infinite plane. Base on the answer provided by @a.lasram, I have produced this implementation, which doest just that: ``` void DrawPlane(const Vector3 & center, const Vector3 & planeNormal, float planeScale, float normalVecScale, const fColorRGBA & planeColor, const fColorRGBA & normalVecColor) { Vector3 tangent, bitangent; OrthogonalBasis(planeNormal, tangent, bitangent); const Vector3 v1(center - (tangent * planeScale) - (bitangent * planeScale)); const Vector3 v2(center + (tangent * planeScale) - (bitangent * planeSc…

Accepted Answer

To see the plane as if it's infinite you can find 4 quad vertices so that the clipped quad and the clipped infinite plane form the same polygon. Example:

Sample 2 random points `P1` and `P2` on the plane such as `P1 != P2`.

Deduce a tangent `t` and bi-tangent `b` as

```
t = normalize(P2-P1); // get a normalized tangent
b = cross(t, n); // the bi-tangent is the cross product of the tangent and the normal
```

Compute the bounding sphere of the view frustum. The sphere would have a diameter `D` (if this step seems difficult, just set `D` to a large enough value such as the corresponding sphere encompasses the frustum).

Get the 4 quad vertices `v1` , `v2` , `v3` and `v4` (CCW or CW depending on the choice of P1 and P2):

```
v1 = P1 - t*D - b*D;
v2 = P1 + t*D - b*D;
v3 = P1 + t*D + b*D;
v4 = P1 - t*D + b*D;
```

Draw arbitrary plane from plane equation, OpenGL

Solution

Problem