Table of Contents
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_xStep 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 × VStep 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 /= lengthApplications in Game Engines
Utilizing perpendicular vectors is pivotal in game physics, such as calculating reflection vectors, implementing friction models, and simulating light.
