Calculating the Surface Area of a Geometric Face in Three.js

Question

Calculating the Surface Area of a Geometric Face in Three.js

When exporting a 3D model using the ColladaLoader, each Mesh generates a Geometry object with multiple Faces.

I have successfully managed to select faces in order to change colors and textures, but now I need to calculate the area of each "Face." Faces are made up of Triangles instances of Face3. I have attempted to loop through each related face and sum the a, b, and c values as shown below, but have not been successful.

var sAB = Math.abs(face.a - face.b);
var sBC = Math.abs(face.b - face.c);
var sCA = Math.abs(face.c - face.a);
var s = sAB + sBC + sCA;
var a = Math.sqrt(s*(s-sAB)*(s-sBC)*(s-sCA));

How can I correctly calculate the area of a Face3 triangle object?

javascript three.js

Answer 1

Answer №1

The Face3 object's values for a, b, and c do not directly store the vertices themselves. Instead, they store the indices of the vertices within geometry.vertices. To access the actual vertices, you would need to do something like this:

var va = geometry.vertices[face.a];
var vb = geometry.vertices[face.b];
var vc = geometry.vertices[face.c];

If you are working with vectors, the calculations cannot be done in the same way. You should utilize the functions available in THREE.Vector3 (e.g.,

var v = new THREE.Vector3(); v.subVectors(va, vb);

) to perform these calculations.

Alternatively, you can also use the THREE.Triangle class for this purpose:

var t = new THREE.Triangle(va, vb, vc);
var area = t.getArea();

Answer 2

The Face3 object's values for a, b, and c do not directly store the vertices themselves. Instead, they store the indices of the vertices within geometry.vertices. To access the actual vertices, you would need to do something like this:

var va = geometry.vertices[face.a];
var vb = geometry.vertices[face.b];
var vc = geometry.vertices[face.c];

If you are working with vectors, the calculations cannot be done in the same way. You should utilize the functions available in THREE.Vector3 (e.g.,

var v = new THREE.Vector3(); v.subVectors(va, vb);

) to perform these calculations.

Alternatively, you can also use the THREE.Triangle class for this purpose:

var t = new THREE.Triangle(va, vb, vc);
var area = t.getArea();

Answer 3

Answer №2

One way to calculate the area of a triangle using Three.js is by using the THREE.Triangle() constructor and its .getArea() method:

var geom = new THREE.PlaneGeometry(1, 1);

var face0 = geom.faces[0]; // Identify the face for which you want to calculate the area

var verts = geom.vertices;

var tri = new THREE.Triangle(verts[face0.a], verts[face0.b], verts[face0.c]);

var area = tri.getArea();
console.log(area);

<script src="https://cdnjs.cloudflare.com/ajax/libs/three.js/93/three.min.js"></script>

Answer 4

One way to calculate the area of a triangle using Three.js is by using the THREE.Triangle() constructor and its .getArea() method:

var geom = new THREE.PlaneGeometry(1, 1);

var face0 = geom.faces[0]; // Identify the face for which you want to calculate the area

var verts = geom.vertices;

var tri = new THREE.Triangle(verts[face0.a], verts[face0.b], verts[face0.c]);

var area = tri.getArea();
console.log(area);

<script src="https://cdnjs.cloudflare.com/ajax/libs/three.js/93/three.min.js"></script>

Answer 5

Answer №3

In addition to the previous responses, from a mathematical standpoint, when you perform a cross product on two vectors, the resulting vector's length will be equivalent to double the area you are trying to calculate. To put it in terms of three.js:

let area = new THREE.Vector3().crossVectors(
    new THREE.Vector3().subVectors(vertexB, vertexA),
    new THREE.Vector3().subVectors(vertexC, vertexA)
).length() / 2;

Answer 6

In addition to the previous responses, from a mathematical standpoint, when you perform a cross product on two vectors, the resulting vector's length will be equivalent to double the area you are trying to calculate. To put it in terms of three.js:

let area = new THREE.Vector3().crossVectors(
    new THREE.Vector3().subVectors(vertexB, vertexA),
    new THREE.Vector3().subVectors(vertexC, vertexA)
).length() / 2;

Answer 7

Answer №4

Innovative ShapeUtils Library offers a helpful function called calculateArea that takes an array of points or vertices representing a 2D polygon:

.area ( contour ) : Number

contour -- 2D polygon.

Estimate the area of a 2D polygon contour.

This feature is similar to the one mentioned by @pailhead, but it functions with polygons containing multiple vertices instead of just three (a triangle).

If you wish to apply this to vertices not restricted to the X-Y plane (extracted from a 3D mesh), it is necessary to rotate/project your mesh beforehand to align it with the X-Y plane. A rotation matrix can assist you in achieving this easily.

Note: Keep in mind that this function has limitations when handling self-intersecting polygons. Refer to the Limitations section on this "Math Resources" website for further details.

Answer 8

Innovative ShapeUtils Library offers a helpful function called calculateArea that takes an array of points or vertices representing a 2D polygon:

.area ( contour ) : Number

contour -- 2D polygon.

Estimate the area of a 2D polygon contour.

This feature is similar to the one mentioned by @pailhead, but it functions with polygons containing multiple vertices instead of just three (a triangle).

If you wish to apply this to vertices not restricted to the X-Y plane (extracted from a 3D mesh), it is necessary to rotate/project your mesh beforehand to align it with the X-Y plane. A rotation matrix can assist you in achieving this easily.

Note: Keep in mind that this function has limitations when handling self-intersecting polygons. Refer to the Limitations section on this "Math Resources" website for further details.

Calculating the Surface Area of a Geometric Face in Three.js

Answer №1

Answer №2

Answer №3

Answer №4

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