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📄 Triangle.js

📊 Analysis Summary

Metric	Count
🔧 Functions	22
🧱 Classes	1
📦 Imports	2
📊 Variables & Constants	26

📚 Table of Contents

• Imports
• Variables & Constants
• Functions
• Classes

🛠️ File Location:

📂 src/math/Triangle.js

📦 Imports

Name	Source
Vector3	./Vector3.js
Vector4	./Vector4.js

---

Variables & Constants

Name	Type	Kind	Value	Exported
_v0	Vector3	let/var	new Vector3()	✗
_v1	Vector3	let/var	new Vector3()	✗
_v2	Vector3	let/var	new Vector3()	✗
_v3	Vector3	let/var	new Vector3()	✗
_vab	Vector3	let/var	new Vector3()	✗
_vac	Vector3	let/var	new Vector3()	✗
_vbc	Vector3	let/var	new Vector3()	✗
_vap	Vector3	let/var	new Vector3()	✗
_vbp	Vector3	let/var	new Vector3()	✗
_vcp	Vector3	let/var	new Vector3()	✗
_v40	Vector4	let/var	new Vector4()	✗
_v41	Vector4	let/var	new Vector4()	✗
_v42	Vector4	let/var	new Vector4()	✗
denom	number	let/var	( dot00 * dot11 - dot01 * dot01 )	✗
invDenom	number	let/var	1 / denom	✗
u	number	let/var	( dot11 * dot02 - dot01 * dot12 ) * invDenom	✗
v	number	let/var	( dot00 * dot12 - dot01 * dot02 ) * invDenom	✗
a	Vector3	let/var	this.a	✗
b	Vector3	let/var	this.b	✗
c	Vector3	let/var	this.c	✗
v	any	let/var	*not shown*	✗
w	any	let/var	*not shown*	✗
vc	number	let/var	d1 * d4 - d3 * d2	✗
vb	number	let/var	d5 * d2 - d1 * d6	✗
va	number	let/var	d3 * d6 - d5 * d4	✗
denom	number	let/var	1 / ( va + vb + vc )	✗

---

Functions

Triangle.getNormal(a: Vector3, b: Vector3, c: Vector3, target: Vector3): Vector3

JSDoc:

/**
     * Computes the normal vector of a triangle.
     *
     * @param {Vector3} a - The first corner of the triangle.
     * @param {Vector3} b - The second corner of the triangle.
     * @param {Vector3} c - The third corner of the triangle.
     * @param {Vector3} target - The target vector that is used to store the method's result.
     * @return {Vector3} The triangle's normal.
     */

Parameters:

• a Vector3
• b Vector3
• c Vector3
• target Vector3

Returns: Vector3

Calls:

• target.subVectors
• _v0.subVectors
• target.cross
• target.lengthSq
• target.multiplyScalar
• Math.sqrt
• target.set

Code

static getNormal( a, b, c, target ) {

        target.subVectors( c, b );
        _v0.subVectors( a, b );
        target.cross( _v0 );

        const targetLengthSq = target.lengthSq();
        if ( targetLengthSq > 0 ) {

            return target.multiplyScalar( 1 / Math.sqrt( targetLengthSq ) );

        }

        return target.set( 0, 0, 0 );

    }

Triangle.getBarycoord(point: Vector3, a: Vector3, b: Vector3, c: Vector3, target: Vector3): Vector3

JSDoc:

/**
     * Computes a barycentric coordinates from the given vector.
     * Returns `null` if the triangle is degenerate.
     *
     * @param {Vector3} point - A point in 3D space.
     * @param {Vector3} a - The first corner of the triangle.
     * @param {Vector3} b - The second corner of the triangle.
     * @param {Vector3} c - The third corner of the triangle.
     * @param {Vector3} target - The target vector that is used to store the method's result.
     * @return {?Vector3} The barycentric coordinates for the given point
     */

Parameters:

• point Vector3
• a Vector3
• b Vector3
• c Vector3
• target Vector3

Returns: Vector3

Calls:

• _v0.subVectors
• _v1.subVectors
• _v2.subVectors
• _v0.dot
• _v1.dot
• target.set

Internal Comments:

// based on: http://www.blackpawn.com/texts/pointinpoly/default.html (x4)
// collinear or singular triangle
// barycentric coordinates must always sum to 1

Code

static getBarycoord( point, a, b, c, target ) {

        // based on: http://www.blackpawn.com/texts/pointinpoly/default.html

        _v0.subVectors( c, a );
        _v1.subVectors( b, a );
        _v2.subVectors( point, a );

        const dot00 = _v0.dot( _v0 );
        const dot01 = _v0.dot( _v1 );
        const dot02 = _v0.dot( _v2 );
        const dot11 = _v1.dot( _v1 );
        const dot12 = _v1.dot( _v2 );

        const denom = ( dot00 * dot11 - dot01 * dot01 );

        // collinear or singular triangle
        if ( denom === 0 ) {

            target.set( 0, 0, 0 );
            return null;

        }

        const invDenom = 1 / denom;
        const u = ( dot11 * dot02 - dot01 * dot12 ) * invDenom;
        const v = ( dot00 * dot12 - dot01 * dot02 ) * invDenom;

        // barycentric coordinates must always sum to 1
        return target.set( 1 - u - v, v, u );

    }

Triangle.containsPoint(point: Vector3, a: Vector3, b: Vector3, c: Vector3): boolean

JSDoc:

/**
     * Returns `true` if the given point, when projected onto the plane of the
     * triangle, lies within the triangle.
     *
     * @param {Vector3} point - The point in 3D space to test.
     * @param {Vector3} a - The first corner of the triangle.
     * @param {Vector3} b - The second corner of the triangle.
     * @param {Vector3} c - The third corner of the triangle.
     * @return {boolean} Whether the given point, when projected onto the plane of the
     * triangle, lies within the triangle or not.
     */

Parameters:

• point Vector3
• a Vector3
• b Vector3
• c Vector3

Returns: boolean

Calls:

• this.getBarycoord

Internal Comments:

// if the triangle is degenerate then we can't contain a point

Code

static containsPoint( point, a, b, c ) {

        // if the triangle is degenerate then we can't contain a point
        if ( this.getBarycoord( point, a, b, c, _v3 ) === null ) {

            return false;

        }

        return ( _v3.x >= 0 ) && ( _v3.y >= 0 ) && ( ( _v3.x + _v3.y ) <= 1 );

    }

Triangle.getInterpolation(point: Vector3, p1: Vector3, p2: Vector3, p3: Vector3, v1: Vector3, v2: Vector3, v3: Vector3, target: Vector3): Vector3

JSDoc:

/**
     * Computes the value barycentrically interpolated for the given point on the
     * triangle. Returns `null` if the triangle is degenerate.
     *
     * @param {Vector3} point - Position of interpolated point.
     * @param {Vector3} p1 - The first corner of the triangle.
     * @param {Vector3} p2 - The second corner of the triangle.
     * @param {Vector3} p3 - The third corner of the triangle.
     * @param {Vector3} v1 - Value to interpolate of first vertex.
     * @param {Vector3} v2 - Value to interpolate of second vertex.
     * @param {Vector3} v3 - Value to interpolate of third vertex.
     * @param {Vector3} target - The target vector that is used to store the method's result.
     * @return {?Vector3} The interpolated value.
     */

Parameters:

• point Vector3
• p1 Vector3
• p2 Vector3
• p3 Vector3
• v1 Vector3
• v2 Vector3
• v3 Vector3
• target Vector3

Returns: Vector3

Calls:

• this.getBarycoord
• target.setScalar
• target.addScaledVector

Code

static getInterpolation( point, p1, p2, p3, v1, v2, v3, target ) {

        if ( this.getBarycoord( point, p1, p2, p3, _v3 ) === null ) {

            target.x = 0;
            target.y = 0;
            if ( 'z' in target ) target.z = 0;
            if ( 'w' in target ) target.w = 0;
            return null;

        }

        target.setScalar( 0 );
        target.addScaledVector( v1, _v3.x );
        target.addScaledVector( v2, _v3.y );
        target.addScaledVector( v3, _v3.z );

        return target;

    }

Triangle.getInterpolatedAttribute(attr: BufferAttribute, i1: number, i2: number, i3: number, barycoord: Vector3, target: Vector3): Vector3

JSDoc:

/**
     * Computes the value barycentrically interpolated for the given attribute and indices.
     *
     * @param {BufferAttribute} attr - The attribute to interpolate.
     * @param {number} i1 - Index of first vertex.
     * @param {number} i2 - Index of second vertex.
     * @param {number} i3 - Index of third vertex.
     * @param {Vector3} barycoord - The barycoordinate value to use to interpolate.
     * @param {Vector3} target - The target vector that is used to store the method's result.
     * @return {Vector3} The interpolated attribute value.
     */

Parameters:

• attr BufferAttribute
• i1 number
• i2 number
• i3 number
• barycoord Vector3
• target Vector3

Returns: Vector3

Calls:

• _v40.setScalar
• _v41.setScalar
• _v42.setScalar
• _v40.fromBufferAttribute
• _v41.fromBufferAttribute
• _v42.fromBufferAttribute
• target.setScalar
• target.addScaledVector

Code

static getInterpolatedAttribute( attr, i1, i2, i3, barycoord, target ) {

        _v40.setScalar( 0 );
        _v41.setScalar( 0 );
        _v42.setScalar( 0 );

        _v40.fromBufferAttribute( attr, i1 );
        _v41.fromBufferAttribute( attr, i2 );
        _v42.fromBufferAttribute( attr, i3 );

        target.setScalar( 0 );
        target.addScaledVector( _v40, barycoord.x );
        target.addScaledVector( _v41, barycoord.y );
        target.addScaledVector( _v42, barycoord.z );

        return target;

    }

Triangle.isFrontFacing(a: Vector3, b: Vector3, c: Vector3, direction: Vector3): boolean

JSDoc:

/**
     * Returns `true` if the triangle is oriented towards the given direction.
     *
     * @param {Vector3} a - The first corner of the triangle.
     * @param {Vector3} b - The second corner of the triangle.
     * @param {Vector3} c - The third corner of the triangle.
     * @param {Vector3} direction - The (normalized) direction vector.
     * @return {boolean} Whether the triangle is oriented towards the given direction or not.
     */

Parameters:

• a Vector3
• b Vector3
• c Vector3
• direction Vector3

Returns: boolean

Calls:

• _v0.subVectors
• _v1.subVectors
• _v0.cross( _v1 ).dot

Internal Comments:

// strictly front facing

Code

static isFrontFacing( a, b, c, direction ) {

        _v0.subVectors( c, b );
        _v1.subVectors( a, b );

        // strictly front facing
        return ( _v0.cross( _v1 ).dot( direction ) < 0 ) ? true : false;

    }

Triangle.set(a: Vector3, b: Vector3, c: Vector3): Triangle

JSDoc:

/**
     * Sets the triangle's vertices by copying the given values.
     *
     * @param {Vector3} a - The first corner of the triangle.
     * @param {Vector3} b - The second corner of the triangle.
     * @param {Vector3} c - The third corner of the triangle.
     * @return {Triangle} A reference to this triangle.
     */

Parameters:

• a Vector3
• b Vector3
• c Vector3

Returns: Triangle

Calls:

• this.a.copy
• this.b.copy
• this.c.copy

Code

set( a, b, c ) {

        this.a.copy( a );
        this.b.copy( b );
        this.c.copy( c );

        return this;

    }

Triangle.setFromPointsAndIndices(points: Vector3[], i0: number, i1: number, i2: number): Triangle

JSDoc:

/**
     * Sets the triangle's vertices by copying the given array values.
     *
     * @param {Array<Vector3>} points - An array with 3D points.
     * @param {number} i0 - The array index representing the first corner of the triangle.
     * @param {number} i1 - The array index representing the second corner of the triangle.
     * @param {number} i2 - The array index representing the third corner of the triangle.
     * @return {Triangle} A reference to this triangle.
     */

Parameters:

• points Vector3[]
• i0 number
• i1 number
• i2 number

Returns: Triangle

Calls:

• this.a.copy
• this.b.copy
• this.c.copy

Code

setFromPointsAndIndices( points, i0, i1, i2 ) {

        this.a.copy( points[ i0 ] );
        this.b.copy( points[ i1 ] );
        this.c.copy( points[ i2 ] );

        return this;

    }

Triangle.setFromAttributeAndIndices(attribute: BufferAttribute, i0: number, i1: number, i2: number): Triangle

JSDoc:

/**
     * Sets the triangle's vertices by copying the given attribute values.
     *
     * @param {BufferAttribute} attribute - A buffer attribute with 3D points data.
     * @param {number} i0 - The attribute index representing the first corner of the triangle.
     * @param {number} i1 - The attribute index representing the second corner of the triangle.
     * @param {number} i2 - The attribute index representing the third corner of the triangle.
     * @return {Triangle} A reference to this triangle.
     */

Parameters:

• attribute BufferAttribute
• i0 number
• i1 number
• i2 number

Returns: Triangle

Calls:

• this.a.fromBufferAttribute
• this.b.fromBufferAttribute
• this.c.fromBufferAttribute

Code

setFromAttributeAndIndices( attribute, i0, i1, i2 ) {

        this.a.fromBufferAttribute( attribute, i0 );
        this.b.fromBufferAttribute( attribute, i1 );
        this.c.fromBufferAttribute( attribute, i2 );

        return this;

    }

Triangle.clone(): Triangle

JSDoc:

/**
     * Returns a new triangle with copied values from this instance.
     *
     * @return {Triangle} A clone of this instance.
     */

Returns: Triangle

Calls:

• new this.constructor().copy

Code

clone() {

        return new this.constructor().copy( this );

    }

Triangle.copy(triangle: Triangle): Triangle

JSDoc:

/**
     * Copies the values of the given triangle to this instance.
     *
     * @param {Triangle} triangle - The triangle to copy.
     * @return {Triangle} A reference to this triangle.
     */

Parameters:

• triangle Triangle

Returns: Triangle

Calls:

• this.a.copy
• this.b.copy
• this.c.copy

Code

copy( triangle ) {

        this.a.copy( triangle.a );
        this.b.copy( triangle.b );
        this.c.copy( triangle.c );

        return this;

    }

Triangle.getArea(): number

JSDoc:

/**
     * Computes the area of the triangle.
     *
     * @return {number} The triangle's area.
     */

Returns: number

Calls:

• _v0.subVectors
• _v1.subVectors
• _v0.cross( _v1 ).length

Code

getArea() {

        _v0.subVectors( this.c, this.b );
        _v1.subVectors( this.a, this.b );

        return _v0.cross( _v1 ).length() * 0.5;

    }

Triangle.getMidpoint(target: Vector3): Vector3

JSDoc:

/**
     * Computes the midpoint of the triangle.
     *
     * @param {Vector3} target - The target vector that is used to store the method's result.
     * @return {Vector3} The triangle's midpoint.
     */

Parameters:

• target Vector3

Returns: Vector3

Calls:

• target.addVectors( this.a, this.b ).add( this.c ).multiplyScalar

Code

getMidpoint( target ) {

        return target.addVectors( this.a, this.b ).add( this.c ).multiplyScalar( 1 / 3 );

    }

Triangle.getNormal(target: Vector3): Vector3

JSDoc:

/**
     * Computes the normal of the triangle.
     *
     * @param {Vector3} target - The target vector that is used to store the method's result.
     * @return {Vector3} The triangle's normal.
     */

Parameters:

• target Vector3

Returns: Vector3

Calls:

• Triangle.getNormal

Code

getNormal( target ) {

        return Triangle.getNormal( this.a, this.b, this.c, target );

    }

Triangle.getPlane(target: Plane): Plane

JSDoc:

/**
     * Computes a plane the triangle lies within.
     *
     * @param {Plane} target - The target vector that is used to store the method's result.
     * @return {Plane} The plane the triangle lies within.
     */

Parameters:

• target Plane

Returns: Plane

Calls:

• target.setFromCoplanarPoints

Code

getPlane( target ) {

        return target.setFromCoplanarPoints( this.a, this.b, this.c );

    }

Triangle.getBarycoord(point: Vector3, target: Vector3): Vector3

JSDoc:

/**
     * Computes a barycentric coordinates from the given vector.
     * Returns `null` if the triangle is degenerate.
     *
     * @param {Vector3} point - A point in 3D space.
     * @param {Vector3} target - The target vector that is used to store the method's result.
     * @return {?Vector3} The barycentric coordinates for the given point
     */

Parameters:

• point Vector3
• target Vector3

Returns: Vector3

Calls:

• Triangle.getBarycoord

Code

getBarycoord( point, target ) {

        return Triangle.getBarycoord( point, this.a, this.b, this.c, target );

    }

Triangle.getInterpolation(point: Vector3, v1: Vector3, v2: Vector3, v3: Vector3, target: Vector3): Vector3

JSDoc:

/**
     * Computes the value barycentrically interpolated for the given point on the
     * triangle. Returns `null` if the triangle is degenerate.
     *
     * @param {Vector3} point - Position of interpolated point.
     * @param {Vector3} v1 - Value to interpolate of first vertex.
     * @param {Vector3} v2 - Value to interpolate of second vertex.
     * @param {Vector3} v3 - Value to interpolate of third vertex.
     * @param {Vector3} target - The target vector that is used to store the method's result.
     * @return {?Vector3} The interpolated value.
     */

Parameters:

• point Vector3
• v1 Vector3
• v2 Vector3
• v3 Vector3
• target Vector3

Returns: Vector3

Calls:

• Triangle.getInterpolation

Code

getInterpolation( point, v1, v2, v3, target ) {

        return Triangle.getInterpolation( point, this.a, this.b, this.c, v1, v2, v3, target );

    }

Triangle.containsPoint(point: Vector3): boolean

JSDoc:

/**
     * Returns `true` if the given point, when projected onto the plane of the
     * triangle, lies within the triangle.
     *
     * @param {Vector3} point - The point in 3D space to test.
     * @return {boolean} Whether the given point, when projected onto the plane of the
     * triangle, lies within the triangle or not.
     */

Parameters:

• point Vector3

Returns: boolean

Calls:

• Triangle.containsPoint

Code

containsPoint( point ) {

        return Triangle.containsPoint( point, this.a, this.b, this.c );

    }

Triangle.isFrontFacing(direction: Vector3): boolean

JSDoc:

/**
     * Returns `true` if the triangle is oriented towards the given direction.
     *
     * @param {Vector3} direction - The (normalized) direction vector.
     * @return {boolean} Whether the triangle is oriented towards the given direction or not.
     */

Parameters:

• direction Vector3

Returns: boolean

Calls:

• Triangle.isFrontFacing

Code

isFrontFacing( direction ) {

        return Triangle.isFrontFacing( this.a, this.b, this.c, direction );

    }

Triangle.intersectsBox(box: Box3): boolean

JSDoc:

/**
     * Returns `true` if this triangle intersects with the given box.
     *
     * @param {Box3} box - The box to intersect.
     * @return {boolean} Whether this triangle intersects with the given box or not.
     */

Parameters:

• box Box3

Returns: boolean

Calls:

• box.intersectsTriangle

Code

intersectsBox( box ) {

        return box.intersectsTriangle( this );

    }

Triangle.closestPointToPoint(p: Vector3, target: Vector3): Vector3

JSDoc:

/**
     * Returns the closest point on the triangle to the given point.
     *
     * @param {Vector3} p - The point to compute the closest point for.
     * @param {Vector3} target - The target vector that is used to store the method's result.
     * @return {Vector3} The closest point on the triangle.
     */

Parameters:

• p Vector3
• target Vector3

Returns: Vector3

Calls:

• _vab.subVectors
• _vac.subVectors
• _vap.subVectors
• _vab.dot
• _vac.dot
• target.copy
• _vbp.subVectors
• target.copy( a ).addScaledVector
• _vcp.subVectors
• _vbc.subVectors
• target.copy( b ).addScaledVector
• target.copy( a ).addScaledVector( _vab, v ).addScaledVector

Internal Comments:

// algorithm thanks to Real-Time Collision Detection by Christer Ericson, (x4)
// published by Morgan Kaufmann Publishers, (c) 2005 Elsevier Inc., (x4)
// under the accompanying license; see chapter 5.1.5 for detailed explanation. (x4)
// basically, we're distinguishing which of the voronoi regions of the triangle (x4)
// the point lies in with the minimum amount of redundant computation. (x4)
// vertex region of A; barycentric coords (1, 0, 0)
// vertex region of B; barycentric coords (0, 1, 0)
// edge region of AB; barycentric coords (1-v, v, 0)
// vertex region of C; barycentric coords (0, 0, 1)
// edge region of AC; barycentric coords (1-w, 0, w)
// edge region of BC; barycentric coords (0, 1-w, w)
// face region (x2)
// u = va * denom (x3)

Code

closestPointToPoint( p, target ) {

        const a = this.a, b = this.b, c = this.c;
        let v, w;

        // algorithm thanks to Real-Time Collision Detection by Christer Ericson,
        // published by Morgan Kaufmann Publishers, (c) 2005 Elsevier Inc.,
        // under the accompanying license; see chapter 5.1.5 for detailed explanation.
        // basically, we're distinguishing which of the voronoi regions of the triangle
        // the point lies in with the minimum amount of redundant computation.

        _vab.subVectors( b, a );
        _vac.subVectors( c, a );
        _vap.subVectors( p, a );
        const d1 = _vab.dot( _vap );
        const d2 = _vac.dot( _vap );
        if ( d1 <= 0 && d2 <= 0 ) {

            // vertex region of A; barycentric coords (1, 0, 0)
            return target.copy( a );

        }

        _vbp.subVectors( p, b );
        const d3 = _vab.dot( _vbp );
        const d4 = _vac.dot( _vbp );
        if ( d3 >= 0 && d4 <= d3 ) {

            // vertex region of B; barycentric coords (0, 1, 0)
            return target.copy( b );

        }

        const vc = d1 * d4 - d3 * d2;
        if ( vc <= 0 && d1 >= 0 && d3 <= 0 ) {

            v = d1 / ( d1 - d3 );
            // edge region of AB; barycentric coords (1-v, v, 0)
            return target.copy( a ).addScaledVector( _vab, v );

        }

        _vcp.subVectors( p, c );
        const d5 = _vab.dot( _vcp );
        const d6 = _vac.dot( _vcp );
        if ( d6 >= 0 && d5 <= d6 ) {

            // vertex region of C; barycentric coords (0, 0, 1)
            return target.copy( c );

        }

        const vb = d5 * d2 - d1 * d6;
        if ( vb <= 0 && d2 >= 0 && d6 <= 0 ) {

            w = d2 / ( d2 - d6 );
            // edge region of AC; barycentric coords (1-w, 0, w)
            return target.copy( a ).addScaledVector( _vac, w );

        }

        const va = d3 * d6 - d5 * d4;
        if ( va <= 0 && ( d4 - d3 ) >= 0 && ( d5 - d6 ) >= 0 ) {

            _vbc.subVectors( c, b );
            w = ( d4 - d3 ) / ( ( d4 - d3 ) + ( d5 - d6 ) );
            // edge region of BC; barycentric coords (0, 1-w, w)
            return target.copy( b ).addScaledVector( _vbc, w ); // edge region of BC

        }

        // face region
        const denom = 1 / ( va + vb + vc );
        // u = va * denom
        v = vb * denom;
        w = vc * denom;

        return target.copy( a ).addScaledVector( _vab, v ).addScaledVector( _vac, w );

    }

Triangle.equals(triangle: Triangle): boolean

JSDoc:

/**
     * Returns `true` if this triangle is equal with the given one.
     *
     * @param {Triangle} triangle - The triangle to test for equality.
     * @return {boolean} Whether this triangle is equal with the given one.
     */

Parameters:

• triangle Triangle

Returns: boolean

Calls:

• triangle.a.equals
• triangle.b.equals
• triangle.c.equals

Code

equals( triangle ) {

        return triangle.a.equals( this.a ) && triangle.b.equals( this.b ) && triangle.c.equals( this.c );

    }

---

Classes

Triangle

Class Code

class Triangle {

    /**
     * Constructs a new triangle.
     *
     * @param {Vector3} [a=(0,0,0)] - The first corner of the triangle.
     * @param {Vector3} [b=(0,0,0)] - The second corner of the triangle.
     * @param {Vector3} [c=(0,0,0)] - The third corner of the triangle.
     */
    constructor( a = new Vector3(), b = new Vector3(), c = new Vector3() ) {

        /**
         * The first corner of the triangle.
         *
         * @type {Vector3}
         */
        this.a = a;

        /**
         * The second corner of the triangle.
         *
         * @type {Vector3}
         */
        this.b = b;

        /**
         * The third corner of the triangle.
         *
         * @type {Vector3}
         */
        this.c = c;

    }

    /**
     * Computes the normal vector of a triangle.
     *
     * @param {Vector3} a - The first corner of the triangle.
     * @param {Vector3} b - The second corner of the triangle.
     * @param {Vector3} c - The third corner of the triangle.
     * @param {Vector3} target - The target vector that is used to store the method's result.
     * @return {Vector3} The triangle's normal.
     */
    static getNormal( a, b, c, target ) {

        target.subVectors( c, b );
        _v0.subVectors( a, b );
        target.cross( _v0 );

        const targetLengthSq = target.lengthSq();
        if ( targetLengthSq > 0 ) {

            return target.multiplyScalar( 1 / Math.sqrt( targetLengthSq ) );

        }

        return target.set( 0, 0, 0 );

    }

    /**
     * Computes a barycentric coordinates from the given vector.
     * Returns `null` if the triangle is degenerate.
     *
     * @param {Vector3} point - A point in 3D space.
     * @param {Vector3} a - The first corner of the triangle.
     * @param {Vector3} b - The second corner of the triangle.
     * @param {Vector3} c - The third corner of the triangle.
     * @param {Vector3} target - The target vector that is used to store the method's result.
     * @return {?Vector3} The barycentric coordinates for the given point
     */
    static getBarycoord( point, a, b, c, target ) {

        // based on: http://www.blackpawn.com/texts/pointinpoly/default.html

        _v0.subVectors( c, a );
        _v1.subVectors( b, a );
        _v2.subVectors( point, a );

        const dot00 = _v0.dot( _v0 );
        const dot01 = _v0.dot( _v1 );
        const dot02 = _v0.dot( _v2 );
        const dot11 = _v1.dot( _v1 );
        const dot12 = _v1.dot( _v2 );

        const denom = ( dot00 * dot11 - dot01 * dot01 );

        // collinear or singular triangle
        if ( denom === 0 ) {

            target.set( 0, 0, 0 );
            return null;

        }

        const invDenom = 1 / denom;
        const u = ( dot11 * dot02 - dot01 * dot12 ) * invDenom;
        const v = ( dot00 * dot12 - dot01 * dot02 ) * invDenom;

        // barycentric coordinates must always sum to 1
        return target.set( 1 - u - v, v, u );

    }

    /**
     * Returns `true` if the given point, when projected onto the plane of the
     * triangle, lies within the triangle.
     *
     * @param {Vector3} point - The point in 3D space to test.
     * @param {Vector3} a - The first corner of the triangle.
     * @param {Vector3} b - The second corner of the triangle.
     * @param {Vector3} c - The third corner of the triangle.
     * @return {boolean} Whether the given point, when projected onto the plane of the
     * triangle, lies within the triangle or not.
     */
    static containsPoint( point, a, b, c ) {

        // if the triangle is degenerate then we can't contain a point
        if ( this.getBarycoord( point, a, b, c, _v3 ) === null ) {

            return false;

        }

        return ( _v3.x >= 0 ) && ( _v3.y >= 0 ) && ( ( _v3.x + _v3.y ) <= 1 );

    }

    /**
     * Computes the value barycentrically interpolated for the given point on the
     * triangle. Returns `null` if the triangle is degenerate.
     *
     * @param {Vector3} point - Position of interpolated point.
     * @param {Vector3} p1 - The first corner of the triangle.
     * @param {Vector3} p2 - The second corner of the triangle.
     * @param {Vector3} p3 - The third corner of the triangle.
     * @param {Vector3} v1 - Value to interpolate of first vertex.
     * @param {Vector3} v2 - Value to interpolate of second vertex.
     * @param {Vector3} v3 - Value to interpolate of third vertex.
     * @param {Vector3} target - The target vector that is used to store the method's result.
     * @return {?Vector3} The interpolated value.
     */
    static getInterpolation( point, p1, p2, p3, v1, v2, v3, target ) {

        if ( this.getBarycoord( point, p1, p2, p3, _v3 ) === null ) {

            target.x = 0;
            target.y = 0;
            if ( 'z' in target ) target.z = 0;
            if ( 'w' in target ) target.w = 0;
            return null;

        }

        target.setScalar( 0 );
        target.addScaledVector( v1, _v3.x );
        target.addScaledVector( v2, _v3.y );
        target.addScaledVector( v3, _v3.z );

        return target;

    }

    /**
     * Computes the value barycentrically interpolated for the given attribute and indices.
     *
     * @param {BufferAttribute} attr - The attribute to interpolate.
     * @param {number} i1 - Index of first vertex.
     * @param {number} i2 - Index of second vertex.
     * @param {number} i3 - Index of third vertex.
     * @param {Vector3} barycoord - The barycoordinate value to use to interpolate.
     * @param {Vector3} target - The target vector that is used to store the method's result.
     * @return {Vector3} The interpolated attribute value.
     */
    static getInterpolatedAttribute( attr, i1, i2, i3, barycoord, target ) {

        _v40.setScalar( 0 );
        _v41.setScalar( 0 );
        _v42.setScalar( 0 );

        _v40.fromBufferAttribute( attr, i1 );
        _v41.fromBufferAttribute( attr, i2 );
        _v42.fromBufferAttribute( attr, i3 );

        target.setScalar( 0 );
        target.addScaledVector( _v40, barycoord.x );
        target.addScaledVector( _v41, barycoord.y );
        target.addScaledVector( _v42, barycoord.z );

        return target;

    }

    /**
     * Returns `true` if the triangle is oriented towards the given direction.
     *
     * @param {Vector3} a - The first corner of the triangle.
     * @param {Vector3} b - The second corner of the triangle.
     * @param {Vector3} c - The third corner of the triangle.
     * @param {Vector3} direction - The (normalized) direction vector.
     * @return {boolean} Whether the triangle is oriented towards the given direction or not.
     */
    static isFrontFacing( a, b, c, direction ) {

        _v0.subVectors( c, b );
        _v1.subVectors( a, b );

        // strictly front facing
        return ( _v0.cross( _v1 ).dot( direction ) < 0 ) ? true : false;

    }

    /**
     * Sets the triangle's vertices by copying the given values.
     *
     * @param {Vector3} a - The first corner of the triangle.
     * @param {Vector3} b - The second corner of the triangle.
     * @param {Vector3} c - The third corner of the triangle.
     * @return {Triangle} A reference to this triangle.
     */
    set( a, b, c ) {

        this.a.copy( a );
        this.b.copy( b );
        this.c.copy( c );

        return this;

    }

    /**
     * Sets the triangle's vertices by copying the given array values.
     *
     * @param {Array<Vector3>} points - An array with 3D points.
     * @param {number} i0 - The array index representing the first corner of the triangle.
     * @param {number} i1 - The array index representing the second corner of the triangle.
     * @param {number} i2 - The array index representing the third corner of the triangle.
     * @return {Triangle} A reference to this triangle.
     */
    setFromPointsAndIndices( points, i0, i1, i2 ) {

        this.a.copy( points[ i0 ] );
        this.b.copy( points[ i1 ] );
        this.c.copy( points[ i2 ] );

        return this;

    }

    /**
     * Sets the triangle's vertices by copying the given attribute values.
     *
     * @param {BufferAttribute} attribute - A buffer attribute with 3D points data.
     * @param {number} i0 - The attribute index representing the first corner of the triangle.
     * @param {number} i1 - The attribute index representing the second corner of the triangle.
     * @param {number} i2 - The attribute index representing the third corner of the triangle.
     * @return {Triangle} A reference to this triangle.
     */
    setFromAttributeAndIndices( attribute, i0, i1, i2 ) {

        this.a.fromBufferAttribute( attribute, i0 );
        this.b.fromBufferAttribute( attribute, i1 );
        this.c.fromBufferAttribute( attribute, i2 );

        return this;

    }

    /**
     * Returns a new triangle with copied values from this instance.
     *
     * @return {Triangle} A clone of this instance.
     */
    clone() {

        return new this.constructor().copy( this );

    }

    /**
     * Copies the values of the given triangle to this instance.
     *
     * @param {Triangle} triangle - The triangle to copy.
     * @return {Triangle} A reference to this triangle.
     */
    copy( triangle ) {

        this.a.copy( triangle.a );
        this.b.copy( triangle.b );
        this.c.copy( triangle.c );

        return this;

    }

    /**
     * Computes the area of the triangle.
     *
     * @return {number} The triangle's area.
     */
    getArea() {

        _v0.subVectors( this.c, this.b );
        _v1.subVectors( this.a, this.b );

        return _v0.cross( _v1 ).length() * 0.5;

    }

    /**
     * Computes the midpoint of the triangle.
     *
     * @param {Vector3} target - The target vector that is used to store the method's result.
     * @return {Vector3} The triangle's midpoint.
     */
    getMidpoint( target ) {

        return target.addVectors( this.a, this.b ).add( this.c ).multiplyScalar( 1 / 3 );

    }

    /**
     * Computes the normal of the triangle.
     *
     * @param {Vector3} target - The target vector that is used to store the method's result.
     * @return {Vector3} The triangle's normal.
     */
    getNormal( target ) {

        return Triangle.getNormal( this.a, this.b, this.c, target );

    }

    /**
     * Computes a plane the triangle lies within.
     *
     * @param {Plane} target - The target vector that is used to store the method's result.
     * @return {Plane} The plane the triangle lies within.
     */
    getPlane( target ) {

        return target.setFromCoplanarPoints( this.a, this.b, this.c );

    }

    /**
     * Computes a barycentric coordinates from the given vector.
     * Returns `null` if the triangle is degenerate.
     *
     * @param {Vector3} point - A point in 3D space.
     * @param {Vector3} target - The target vector that is used to store the method's result.
     * @return {?Vector3} The barycentric coordinates for the given point
     */
    getBarycoord( point, target ) {

        return Triangle.getBarycoord( point, this.a, this.b, this.c, target );

    }

    /**
     * Computes the value barycentrically interpolated for the given point on the
     * triangle. Returns `null` if the triangle is degenerate.
     *
     * @param {Vector3} point - Position of interpolated point.
     * @param {Vector3} v1 - Value to interpolate of first vertex.
     * @param {Vector3} v2 - Value to interpolate of second vertex.
     * @param {Vector3} v3 - Value to interpolate of third vertex.
     * @param {Vector3} target - The target vector that is used to store the method's result.
     * @return {?Vector3} The interpolated value.
     */
    getInterpolation( point, v1, v2, v3, target ) {

        return Triangle.getInterpolation( point, this.a, this.b, this.c, v1, v2, v3, target );

    }

    /**
     * Returns `true` if the given point, when projected onto the plane of the
     * triangle, lies within the triangle.
     *
     * @param {Vector3} point - The point in 3D space to test.
     * @return {boolean} Whether the given point, when projected onto the plane of the
     * triangle, lies within the triangle or not.
     */
    containsPoint( point ) {

        return Triangle.containsPoint( point, this.a, this.b, this.c );

    }

    /**
     * Returns `true` if the triangle is oriented towards the given direction.
     *
     * @param {Vector3} direction - The (normalized) direction vector.
     * @return {boolean} Whether the triangle is oriented towards the given direction or not.
     */
    isFrontFacing( direction ) {

        return Triangle.isFrontFacing( this.a, this.b, this.c, direction );

    }

    /**
     * Returns `true` if this triangle intersects with the given box.
     *
     * @param {Box3} box - The box to intersect.
     * @return {boolean} Whether this triangle intersects with the given box or not.
     */
    intersectsBox( box ) {

        return box.intersectsTriangle( this );

    }

    /**
     * Returns the closest point on the triangle to the given point.
     *
     * @param {Vector3} p - The point to compute the closest point for.
     * @param {Vector3} target - The target vector that is used to store the method's result.
     * @return {Vector3} The closest point on the triangle.
     */
    closestPointToPoint( p, target ) {

        const a = this.a, b = this.b, c = this.c;
        let v, w;

        // algorithm thanks to Real-Time Collision Detection by Christer Ericson,
        // published by Morgan Kaufmann Publishers, (c) 2005 Elsevier Inc.,
        // under the accompanying license; see chapter 5.1.5 for detailed explanation.
        // basically, we're distinguishing which of the voronoi regions of the triangle
        // the point lies in with the minimum amount of redundant computation.

        _vab.subVectors( b, a );
        _vac.subVectors( c, a );
        _vap.subVectors( p, a );
        const d1 = _vab.dot( _vap );
        const d2 = _vac.dot( _vap );
        if ( d1 <= 0 && d2 <= 0 ) {

            // vertex region of A; barycentric coords (1, 0, 0)
            return target.copy( a );

        }

        _vbp.subVectors( p, b );
        const d3 = _vab.dot( _vbp );
        const d4 = _vac.dot( _vbp );
        if ( d3 >= 0 && d4 <= d3 ) {

            // vertex region of B; barycentric coords (0, 1, 0)
            return target.copy( b );

        }

        const vc = d1 * d4 - d3 * d2;
        if ( vc <= 0 && d1 >= 0 && d3 <= 0 ) {

            v = d1 / ( d1 - d3 );
            // edge region of AB; barycentric coords (1-v, v, 0)
            return target.copy( a ).addScaledVector( _vab, v );

        }

        _vcp.subVectors( p, c );
        const d5 = _vab.dot( _vcp );
        const d6 = _vac.dot( _vcp );
        if ( d6 >= 0 && d5 <= d6 ) {

            // vertex region of C; barycentric coords (0, 0, 1)
            return target.copy( c );

        }

        const vb = d5 * d2 - d1 * d6;
        if ( vb <= 0 && d2 >= 0 && d6 <= 0 ) {

            w = d2 / ( d2 - d6 );
            // edge region of AC; barycentric coords (1-w, 0, w)
            return target.copy( a ).addScaledVector( _vac, w );

        }

        const va = d3 * d6 - d5 * d4;
        if ( va <= 0 && ( d4 - d3 ) >= 0 && ( d5 - d6 ) >= 0 ) {

            _vbc.subVectors( c, b );
            w = ( d4 - d3 ) / ( ( d4 - d3 ) + ( d5 - d6 ) );
            // edge region of BC; barycentric coords (0, 1-w, w)
            return target.copy( b ).addScaledVector( _vbc, w ); // edge region of BC

        }

        // face region
        const denom = 1 / ( va + vb + vc );
        // u = va * denom
        v = vb * denom;
        w = vc * denom;

        return target.copy( a ).addScaledVector( _vab, v ).addScaledVector( _vac, w );

    }

    /**
     * Returns `true` if this triangle is equal with the given one.
     *
     * @param {Triangle} triangle - The triangle to test for equality.
     * @return {boolean} Whether this triangle is equal with the given one.
     */
    equals( triangle ) {

        return triangle.a.equals( this.a ) && triangle.b.equals( this.b ) && triangle.c.equals( this.c );

    }

}

Methods

getNormal(a: Vector3, b: Vector3, c: Vector3, target: Vector3): Vector3

Code

static getNormal( a, b, c, target ) {

        target.subVectors( c, b );
        _v0.subVectors( a, b );
        target.cross( _v0 );

        const targetLengthSq = target.lengthSq();
        if ( targetLengthSq > 0 ) {

            return target.multiplyScalar( 1 / Math.sqrt( targetLengthSq ) );

        }

        return target.set( 0, 0, 0 );

    }

getBarycoord(point: Vector3, a: Vector3, b: Vector3, c: Vector3, target: Vector3): Vector3

Code

static getBarycoord( point, a, b, c, target ) {

        // based on: http://www.blackpawn.com/texts/pointinpoly/default.html

        _v0.subVectors( c, a );
        _v1.subVectors( b, a );
        _v2.subVectors( point, a );

        const dot00 = _v0.dot( _v0 );
        const dot01 = _v0.dot( _v1 );
        const dot02 = _v0.dot( _v2 );
        const dot11 = _v1.dot( _v1 );
        const dot12 = _v1.dot( _v2 );

        const denom = ( dot00 * dot11 - dot01 * dot01 );

        // collinear or singular triangle
        if ( denom === 0 ) {

            target.set( 0, 0, 0 );
            return null;

        }

        const invDenom = 1 / denom;
        const u = ( dot11 * dot02 - dot01 * dot12 ) * invDenom;
        const v = ( dot00 * dot12 - dot01 * dot02 ) * invDenom;

        // barycentric coordinates must always sum to 1
        return target.set( 1 - u - v, v, u );

    }

containsPoint(point: Vector3, a: Vector3, b: Vector3, c: Vector3): boolean

Code

static containsPoint( point, a, b, c ) {

        // if the triangle is degenerate then we can't contain a point
        if ( this.getBarycoord( point, a, b, c, _v3 ) === null ) {

            return false;

        }

        return ( _v3.x >= 0 ) && ( _v3.y >= 0 ) && ( ( _v3.x + _v3.y ) <= 1 );

    }

getInterpolation(point: Vector3, p1: Vector3, p2: Vector3, p3: Vector3, v1: Vector3, v2: Vector3, v3: Vector3, target: Vector3): Vector3

Code

static getInterpolation( point, p1, p2, p3, v1, v2, v3, target ) {

        if ( this.getBarycoord( point, p1, p2, p3, _v3 ) === null ) {

            target.x = 0;
            target.y = 0;
            if ( 'z' in target ) target.z = 0;
            if ( 'w' in target ) target.w = 0;
            return null;

        }

        target.setScalar( 0 );
        target.addScaledVector( v1, _v3.x );
        target.addScaledVector( v2, _v3.y );
        target.addScaledVector( v3, _v3.z );

        return target;

    }

getInterpolatedAttribute(attr: BufferAttribute, i1: number, i2: number, i3: number, barycoord: Vector3, target: Vector3): Vector3

Code

static getInterpolatedAttribute( attr, i1, i2, i3, barycoord, target ) {

        _v40.setScalar( 0 );
        _v41.setScalar( 0 );
        _v42.setScalar( 0 );

        _v40.fromBufferAttribute( attr, i1 );
        _v41.fromBufferAttribute( attr, i2 );
        _v42.fromBufferAttribute( attr, i3 );

        target.setScalar( 0 );
        target.addScaledVector( _v40, barycoord.x );
        target.addScaledVector( _v41, barycoord.y );
        target.addScaledVector( _v42, barycoord.z );

        return target;

    }

isFrontFacing(a: Vector3, b: Vector3, c: Vector3, direction: Vector3): boolean

Code

static isFrontFacing( a, b, c, direction ) {

        _v0.subVectors( c, b );
        _v1.subVectors( a, b );

        // strictly front facing
        return ( _v0.cross( _v1 ).dot( direction ) < 0 ) ? true : false;

    }

set(a: Vector3, b: Vector3, c: Vector3): Triangle

Code

set( a, b, c ) {

        this.a.copy( a );
        this.b.copy( b );
        this.c.copy( c );

        return this;

    }

setFromPointsAndIndices(points: Vector3[], i0: number, i1: number, i2: number): Triangle

Code

setFromPointsAndIndices( points, i0, i1, i2 ) {

        this.a.copy( points[ i0 ] );
        this.b.copy( points[ i1 ] );
        this.c.copy( points[ i2 ] );

        return this;

    }

setFromAttributeAndIndices(attribute: BufferAttribute, i0: number, i1: number, i2: number): Triangle

Code

setFromAttributeAndIndices( attribute, i0, i1, i2 ) {

        this.a.fromBufferAttribute( attribute, i0 );
        this.b.fromBufferAttribute( attribute, i1 );
        this.c.fromBufferAttribute( attribute, i2 );

        return this;

    }

clone(): Triangle

Code

clone() {

        return new this.constructor().copy( this );

    }

copy(triangle: Triangle): Triangle

Code

copy( triangle ) {

        this.a.copy( triangle.a );
        this.b.copy( triangle.b );
        this.c.copy( triangle.c );

        return this;

    }

getArea(): number

Code

getArea() {

        _v0.subVectors( this.c, this.b );
        _v1.subVectors( this.a, this.b );

        return _v0.cross( _v1 ).length() * 0.5;

    }

getMidpoint(target: Vector3): Vector3

Code

getMidpoint( target ) {

        return target.addVectors( this.a, this.b ).add( this.c ).multiplyScalar( 1 / 3 );

    }

getNormal(target: Vector3): Vector3

Code

getNormal( target ) {

        return Triangle.getNormal( this.a, this.b, this.c, target );

    }

getPlane(target: Plane): Plane

Code

getPlane( target ) {

        return target.setFromCoplanarPoints( this.a, this.b, this.c );

    }

getBarycoord(point: Vector3, target: Vector3): Vector3

Code

getBarycoord( point, target ) {

        return Triangle.getBarycoord( point, this.a, this.b, this.c, target );

    }

getInterpolation(point: Vector3, v1: Vector3, v2: Vector3, v3: Vector3, target: Vector3): Vector3

Code

getInterpolation( point, v1, v2, v3, target ) {

        return Triangle.getInterpolation( point, this.a, this.b, this.c, v1, v2, v3, target );

    }

containsPoint(point: Vector3): boolean

Code

containsPoint( point ) {

        return Triangle.containsPoint( point, this.a, this.b, this.c );

    }

isFrontFacing(direction: Vector3): boolean

Code

isFrontFacing( direction ) {

        return Triangle.isFrontFacing( this.a, this.b, this.c, direction );

    }

intersectsBox(box: Box3): boolean

Code

intersectsBox( box ) {

        return box.intersectsTriangle( this );

    }

closestPointToPoint(p: Vector3, target: Vector3): Vector3

Code

closestPointToPoint( p, target ) {

        const a = this.a, b = this.b, c = this.c;
        let v, w;

        // algorithm thanks to Real-Time Collision Detection by Christer Ericson,
        // published by Morgan Kaufmann Publishers, (c) 2005 Elsevier Inc.,
        // under the accompanying license; see chapter 5.1.5 for detailed explanation.
        // basically, we're distinguishing which of the voronoi regions of the triangle
        // the point lies in with the minimum amount of redundant computation.

        _vab.subVectors( b, a );
        _vac.subVectors( c, a );
        _vap.subVectors( p, a );
        const d1 = _vab.dot( _vap );
        const d2 = _vac.dot( _vap );
        if ( d1 <= 0 && d2 <= 0 ) {

            // vertex region of A; barycentric coords (1, 0, 0)
            return target.copy( a );

        }

        _vbp.subVectors( p, b );
        const d3 = _vab.dot( _vbp );
        const d4 = _vac.dot( _vbp );
        if ( d3 >= 0 && d4 <= d3 ) {

            // vertex region of B; barycentric coords (0, 1, 0)
            return target.copy( b );

        }

        const vc = d1 * d4 - d3 * d2;
        if ( vc <= 0 && d1 >= 0 && d3 <= 0 ) {

            v = d1 / ( d1 - d3 );
            // edge region of AB; barycentric coords (1-v, v, 0)
            return target.copy( a ).addScaledVector( _vab, v );

        }

        _vcp.subVectors( p, c );
        const d5 = _vab.dot( _vcp );
        const d6 = _vac.dot( _vcp );
        if ( d6 >= 0 && d5 <= d6 ) {

            // vertex region of C; barycentric coords (0, 0, 1)
            return target.copy( c );

        }

        const vb = d5 * d2 - d1 * d6;
        if ( vb <= 0 && d2 >= 0 && d6 <= 0 ) {

            w = d2 / ( d2 - d6 );
            // edge region of AC; barycentric coords (1-w, 0, w)
            return target.copy( a ).addScaledVector( _vac, w );

        }

        const va = d3 * d6 - d5 * d4;
        if ( va <= 0 && ( d4 - d3 ) >= 0 && ( d5 - d6 ) >= 0 ) {

            _vbc.subVectors( c, b );
            w = ( d4 - d3 ) / ( ( d4 - d3 ) + ( d5 - d6 ) );
            // edge region of BC; barycentric coords (0, 1-w, w)
            return target.copy( b ).addScaledVector( _vbc, w ); // edge region of BC

        }

        // face region
        const denom = 1 / ( va + vb + vc );
        // u = va * denom
        v = vb * denom;
        w = vc * denom;

        return target.copy( a ).addScaledVector( _vab, v ).addScaledVector( _vac, w );

    }

equals(triangle: Triangle): boolean

Code

equals( triangle ) {

        return triangle.a.equals( this.a ) && triangle.b.equals( this.b ) && triangle.c.equals( this.c );

    }

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