Point4d Class

4 Dimensional point (x,y,z,w) used in perspective calculations.

• the coordinates are stored in a Float64Array of length 4.
• properties x, y, z, w access array members.
• The coordinates are physically stored as a single Float64Array with 4 entries. (w last)

Extends

• Plane3d

Implements

• BeJSONFunctions

Methods

Name	Description
constructor(x: number0, y: number0, z: number0, w: number0): Point4d Protected	Construct from coordinates.
altitude(point: Point3d): number	dotProduct with (point.x, point.y, point.z, 1) Used in PlaneAltitudeEvaluator interface
altitudeXYZ(x: number, y: number, z: number): number	dotProduct with (x, y, z, 1) Used in PlaneAltitudeEvaluator interface
clone(result?: Point4d): Point4d	Clone this point
crossWeightedMinus(other: Point4d, result?: Vector3d): Vector3d	Return ((other.w * this) - (this.w * other))
crossWeightedMinusPoint3d(other: Point3d, result?: Vector3d): Vector3d	Return ((other.w * this) - (this.w * other)), with other.w known to be 1
distanceSquaredXYZW(other: Point4d): number	Return the squared 4d distance from this point to other, with all 4 components squared into the hypotenuse.
distanceXYZW(other: Point4d): number	Return the 4d distance from this point to other, with all 4 components squared into the hypotenuse.
dotProduct(other: Point4d): number	return (4d) dot product of the instance and other point.
dotProductXYZW(x: number, y: number, z: number, w: number): number	return (4d) dot product of the instance with xyzw
dotVectorsToTargets(targetA: Point4d, targetB: Point4d): number	Return dot product of (4d) vectors from the instance to targetA and targetB
interpolate(fraction: number, pointB: Point4d, result?: Point4d): Point4d	Return interpolation between instance and pointB at fraction
isAlmostEqual(other: Point4d): boolean	Near-equality test, using Geometry.isSameCoordinate on all 4 x,y,z,w
isAlmostEqualXYZW(x: number, y: number, z: number, w: number): boolean	Test for same coordinate by direct x,y,z,w args
magnitudeSquaredXYZ(): number	Returns the magnitude of the leading xyz components.
magnitudeXYZW(): number	Returns the magnitude including all 4 components x,y,z,w
maxAbs(): number	Return the largest absolute entry of all 4 components x,y,z,w
maxDiff(other: Point4d): number	Return the largest absolute distance between corresponding components
minus(other: Point4d, result?: Point4d): Point4d	Return the difference (this-other) using all 4 components x,y,z,w
negate(result?: Point4d): Point4d	Negate components (including w!!)
normalX(): number	Return the x component of the normal used to evaluate altitude.
normalY(): number	Return the x component of the normal used to evaluate altitude.
normalZ(): number	Return the z component of the normal used to evaluate altitude.
normalizeQuaternion(): number	Normalize so sum of squares of all 4 coordinates is 1.
normalizeWeight(result?: Point4d): undefined | Point4d	If this.w is nonzero, return a 4d point (x/w,y/w,z/w, 1)
normalizeXYZW(result?: Point4d): undefined | Point4d	divide all components (x,y,z,w) by the 4d magnitude.
plus(other: Point4d, result?: Point4d): Point4d	Return the sum of this and other, using all 4 components x,y,z,w
plus2Scaled(vectorA: Point4d, scalarA: number, vectorB: Point4d, scalarB: number, result?: Point4d): Point4d	Return point + vectorA * scalarA + vectorB * scalarB
plus3Scaled(vectorA: Point4d, scalarA: number, vectorB: Point4d, scalarB: number, vectorC: Point4d, scalarC: number, result?: Point4d): Point4d	Return point + vectorA * scalarA + vectorB * scalarB + vectorC * scalarC
plusScaled(vector: Point4d, scaleFactor: number, result?: Point4d): Point4d	Return point + vector * scalar
projectPointToPlane(spacePoint: Point3d, result?: Point3d): Point3d	* Return xyz projection of spacePoint to the plane (this Point4d is understood as plane coefficients, not point coordinates)
radiansToPoint4dXYZW(other: Point4d): undefined | number	Measure the "angle" between two points, using all 4 components in the dot product that
realDistanceXY(other: Point4d): undefined | number	Return the distance between the instance and other after normalizing by weights
realPoint(result?: Point3d): undefined | Point3d	If this.w is nonzero, return a 3d point (x/w,y/w,z/w)
realPointDefault000(result?: Point3d): Point3d	* If this.w is nonzero, return Point3d with x/w,y/w,z/w.
realPointOrVector(): Point3d | Vector3d	Convert the homogeneous point to a (strongly typed) point or vector.
safeDivideOrNull(denominator: number, result?: Point4d): undefined | Point4d	Divide by denominator, but return undefined if denominator is zero.
scale(scale: number, result?: Point4d): Point4d	scale all components (including w!!)
set(x: number0, y: number0, z: number0, w: number0): Point4d	Set x,y,z,w of this point.
setComponent(index: number, value: number): void	Set a component by index.
setFrom(other: Point4d): Point4d	Copy coordinates from other.
setFromJSON(json?: Point4dProps): void	Set this point's xyzw from a json array [x,y,z,w]
toJSON(): Point4dProps	Convert an Angle to a JSON object.
toPlane3dByOriginAndUnitNormal(result?: Plane3dByOriginAndUnitNormal): undefined | Plane3dByOriginAndUnitNormal	Treating this Point4d as plane coefficients, convert to origin and normal form.
velocity(vector: Vector3d): number	dotProduct with (vector.x, vector.y, vector.z, 0).
velocityXYZ(x: number, y: number, z: number): number	dotProduct with (x,y,z, 0).
weightedAltitude(point: Point4d): number	dotProduct with (point.x, point.y, point.z, point.w) Used in PlaneAltitudeEvaluator interface
create(x: number0, y: number0, z: number0, w: number0, result?: Point4d): Point4d Static	Return a Point4d with specified x,y,z,w
createAdd2Scaled(vectorA: Point4d, scalarA: number, vectorB: Point4d, scalarB: number, result?: Point4d): Point4d Static	Return point + vectorA * scalarA + vectorB * scalarB
createAdd3Scaled(vectorA: Point4d, scalarA: number, vectorB: Point4d, scalarB: number, vectorC: Point4d, scalarC: number, result?: Point4d): Point4d Static	Return point + vectorA \ scalarA + vectorB * scalarB + vectorC * scalarC
createFromPacked(data: Float64Array, xIndex: number0, result?: Point4d): undefined | Point4d Static	extract 4 consecutive numbers from a Float64Array into a Point4d.
createFromPackedXYZ(data: Float64Array, xIndex: number0, result?: Point4d): undefined | Point4d Static	extract 3 consecutive numbers from a Float64Array into the xyz values of a Point4d with w = 1.
createFromPackedXYZW(data: Float64Array, xIndex: number0, result?: Point4d): Point4d Static	extract 4 consecutive numbers from a Float64Array into a Point4d.	Deprecated
createFromPoint(point: number[] | Readonly<WritableXAndY> | Readonly<WritableXYAndZ> | Point4d): Point4d Static	Create a Point4d from
createFromPointAndWeight(xyz: Readonly<WritableXYAndZ>, w: number): Point4d Static	Create a Point4d with x,y,z from an XYAndZ input, and w from a separate number.
createPlaneFrom(source: PlaneAltitudeEvaluator): undefined | Point4d Static	Create a "Point4d as a plane" from "any" other PlaneAltitudeEvaluator type.
createPlanePointPointZ(pointA: Point4d, pointB: Point4d, result?: Point4d): Point4d Static	Create plane coefficients for the plane containing pointA, pointB, and 0010.
createRealDerivativePlane3dByOriginAndVectorsDefault000(x: number, y: number, z: number, w: number, dx: number, dy: number, dz: number, dw: number, ddx: number, ddy: number, ddz: number, ddw: number, result?: Plane3dByOriginAndVectors): Plane3dByOriginAndVectors Static	* If w is nonzero, return Vector3d which is the derivative of the projected xyz with given w and 4d derivatives.
createRealDerivativeRay3dDefault000(x: number, y: number, z: number, w: number, dx: number, dy: number, dz: number, dw: number, result?: Ray3d): Ray3d Static	* If w is nonzero, return Vector3d which is the derivative of the projected xyz with given w and 4d derivatives.
createRealPoint3dDefault000(x: number, y: number, z: number, w: number, result?: Point3d): Point3d Static	* If w is nonzero, return Point3d with x/w,y/w,z/w.
createZero(): Point4d Static	Create a point with zero in all coordinates.
determinantIndexed3X3(pointA: Point4d, pointB: Point4d, pointC: Point4d, i: number, j: number, k: number): number Static	Return the determinant of the 3x3 matrix using components i,j,k of the 3 inputs.
fromJSON(json?: Point4dProps): Point4d Static	Create a new point with coordinates from a json array [x,y,z,w]
interpolateQuaternions(quaternion0: Point4d, fractionParameter: number, quaternion1: Point4d, result?: Point4d): Point4d Static	Return a (normalized) quaternion interpolated between two quaternions.
perpendicularPoint4dPlane(pointA: Point4d, pointB: Point4d, pointC: Point4d): Point4d Static	Return a Point4d perpendicular to all 3 inputs.
unitW(): Point4d Static	unit W vector
unitX(): Point4d Static	unit X vector
unitY(): Point4d Static	unit Y vector
unitZ(): Point4d Static	unit Z vector

Inherited methods

Name	Inherited from	Description
classifyAltitude(point: Point3d, tolerance: numberGeometry.smallMetricDistance): "0" | "1" | "-1"	Plane3d	Return a value -1, 0, 1 giving a signed indicator of whether the toleranced altitude of the point is
classifyAltitudeXYZ(x: number, y: number, z: number, tolerance: numberGeometry.smallMetricDistance): "0" | "1" | "-1"	Plane3d	Return a value -1, 0, 1 giving a signed indicator of whether the toleranced altitude of x,y,z is
getAnyPointOnPlane(result?: Point3d): Point3d	Plane3d	Return any point on the plane.
getUnitNormal(result?: Vector3d): undefined | Vector3d	Plane3d	Return the unit normal for the plane.
isPointInPlane(spacePoint: Point3d, tolerance: numberGeometry.smallMetricDistance): boolean	Plane3d	Returns true if spacePoint is within distance tolerance of the plane.

Properties

Name	Type	Description
isAlmostZero Accessor ReadOnly	boolean	Test if all components are nearly zero.
w Accessor	number	The w component of this point.
x Accessor	number	The x component.
xyzw	Float64Array	x,y,z,w are packed into a Float64Array
y Accessor	number	The y component.
z Accessor	number	The z component.

Defined in

• geometry4d/Point4d.ts Line 46