Find normal vector of the triangle faces on the mesh

In Julia, there are multiple ways to find the normal vector of the triangle faces on a mesh. In this article, we will explore three different approaches to solve this problem.

Approach 1: Cross Product

One way to find the normal vector of a triangle face is by using the cross product of two of its edges. Let’s assume we have a triangle with vertices A, B, and C. The cross product of the vectors AB and AC will give us the normal vector.

function find_normal_vector(vertices)
    AB = vertices[2] - vertices[1]
    AC = vertices[3] - vertices[1]
    normal_vector = cross(AB, AC)
    return normal_vector
end

# Example usage
vertices = [ [1, 2, 3], [4, 5, 6], [7, 8, 9] ]
normal_vector = find_normal_vector(vertices)
println(normal_vector)

This approach calculates the normal vector based on the geometry of the triangle. It is a straightforward and efficient method.

Approach 2: Surface Normal Calculation

Another way to find the normal vector of a triangle face is by using the surface normal calculation. This method involves calculating the average of the normals of all the triangles that share a vertex.

function find_normal_vector(vertices)
    normal_vector = [0, 0, 0]
    for i in 1:length(vertices)
        normal_vector += vertices[i]
    end
    normal_vector /= length(vertices)
    return normal_vector
end

# Example usage
vertices = [ [1, 2, 3], [4, 5, 6], [7, 8, 9] ]
normal_vector = find_normal_vector(vertices)
println(normal_vector)

This approach calculates the normal vector based on the average of the vertex normals. It is useful when dealing with complex meshes where the triangles may not have consistent orientations.

Approach 3: Mesh Normal Calculation

The third approach involves using a mesh library to calculate the normal vector of the triangle faces. The MeshIO.jl library provides functions to load and manipulate mesh data.

using MeshIO

function find_normal_vector(mesh)
    normals = MeshIO.normals(mesh)
    return normals
end

# Example usage
mesh = MeshIO.load("mesh.obj")
normal_vector = find_normal_vector(mesh)
println(normal_vector)

This approach relies on external libraries and is suitable when working with complex mesh data. It provides more advanced features and flexibility.

After exploring these three approaches, it is evident that the best option depends on the specific requirements of the problem. If simplicity and efficiency are the main concerns, the cross product method (Approach 1) is recommended. However, if dealing with complex meshes or requiring advanced features, using a mesh library (Approach 3) would be a better choice.