How can I calculate a vector perpendicular to a surface normal for realistic physics simulation in my game engine?

Calculating a Perpendicular Vector to a Surface Normal

In 3D game development, calculating a vector that is perpendicular to a given surface normal is a common requirement for implementing realistic physics simulations. This involves finding a vector that lies on the plane defined by the normal vector.

Step 1: Understanding the Cross Product

The cross product of two vectors results in a third vector that is perpendicular to the plane containing the first two vectors. Mathematically, the cross product c = a × b can be calculated using the formula:

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c_x = a_y * b_z - a_z * b_y
c_y = a_z * b_x - a_x * b_z
c_z = a_x * b_y - a_y * b_x

Step 2: Choosing an Arbitrary Vector

To derive a perpendicular vector p, choose an arbitrary vector that is not parallel to the normal. A common choice is the unit vector (1, 0, 0) or (0, 1, 0) depending on the orientation of the normal vector.

Step 3: Perform the Cross Product Calculation

Perform the cross product between the surface normal N and the arbitrary vector V to obtain the perpendicular vector P:

P = N × V

Step 4: Normalizing the Perpendicular Vector

Once P is computed, normalize it to ensure it’s a unit vector which is often necessary for physics calculations:

length = sqrt(P_x^2 + P_y^2 + P_z^2)
P_x /= length
P_y /= length
P_z /= length

Applications in Game Engines

Utilizing perpendicular vectors is pivotal in game physics, such as calculating reflection vectors, implementing friction models, and simulating light.