CODEWITHSUNDEEP
c++3dgeometryglm-math
Mohamed Moussa
Mohamed Moussa

Reputation: 103

Check if 3D point inside a box

I have a box which consists of 8 vertices and may be scaled or rotated in any direction so I apply the transformation matrix for vertices each transformation, I have center, size and directions on X,Y and Z from center, how can I check if any 3D point is inside the box ?

Upvotes: 0

Views: 3083

Answers (1)

HolyBlackCat
HolyBlackCat

Reputation: 96176

If you have:

vec3 center; // Center of the box.
vec3 dx, dy, dz; // X,Y, and Z directions, normalized.
vec3 half; // Box size in each dimension, divided by 2.

vec3 point; // Point to test.

Then the test is as simple as:

vec3 d = point - center;
bool inside = abs(dot(d, dx)) <= half.x &&
              abs(dot(d, dy)) <= half.y &&
              abs(dot(d, dz)) <= half.z;

The primary property of dot product is that fact that X⋅Y == |X|⋅|Y|⋅cos(angle_formed_by_X_and_Y).

If Y is normalized, then X⋅Y essentially gives you the length of the projection of X onto Y (which is negative iff the angle formed by X and Y is obtuse). Once you have the projection lengths, you just need to compare their absolute values with corresponding half-extents of your box.

Upvotes: 5

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