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import { Base } from "../inputs/base-inputs";
import * as Inputs from "../inputs";
import { MathBitByBit } from "./math";
import { Vector } from "./vector";
/**
* Transformations help to move, scale, rotate objects. You can combine multiple transformations
* for object to be placed exactly into position and orientation that you want.
* Contains various methods for transformations that represent 4x4 matrixes in flat 16 number arrays.
*/
export class Transforms {
constructor(private readonly vector: Vector, private readonly math: MathBitByBit) { }
/**
* Creates rotation transformations around a center point and custom axis.
* Combines translation to origin, axis rotation, then translation back.
* Example: center=[5,0,0], axis=[0,1,0], angle=90° → rotates around vertical axis through point [5,0,0]
* @param inputs Rotation around center with an axis information
* @returns array of transformations
* @group rotation
* @shortname center axis
* @drawable false
*/
rotationCenterAxis(inputs: Inputs.Transforms.RotationCenterAxisDto): Base.TransformMatrixes {
return [
this.translation(-inputs.center[0], -inputs.center[1], -inputs.center[2]),
this.rotationAxis(
inputs.axis,
this.math.degToRad({ number: inputs.angle })
),
this.translation(inputs.center[0], inputs.center[1], inputs.center[2]),
] as Base.TransformMatrixes;
}
/**
* Creates rotation transformations around a center point along the X axis.
* Example: center=[5,5,5], angle=90° → rotates 90° around X axis through point [5,5,5]
* @param inputs Rotation around center with an X axis information
* @returns array of transformations
* @group rotation
* @shortname center x
* @drawable false
*/
rotationCenterX(inputs: Inputs.Transforms.RotationCenterDto): Base.TransformMatrixes {
return [
this.translation(-inputs.center[0], -inputs.center[1], -inputs.center[2]),
this.rotationX(this.math.degToRad({ number: inputs.angle })),
this.translation(inputs.center[0], inputs.center[1], inputs.center[2]),
] as Base.TransformMatrixes;
}
/**
* Creates rotation transformations around a center point along the Y axis.
* Example: center=[0,0,0], angle=45° → rotates 45° around Y axis through origin
* @param inputs Rotation around center with an Y axis information
* @returns array of transformations
* @group rotation
* @shortname center y
* @drawable false
*/
rotationCenterY(inputs: Inputs.Transforms.RotationCenterDto): Base.TransformMatrixes {
return [
this.translation(-inputs.center[0], -inputs.center[1], -inputs.center[2]),
this.rotationY(this.math.degToRad({ number: inputs.angle })),
this.translation(inputs.center[0], inputs.center[1], inputs.center[2]),
] as Base.TransformMatrixes;
}
/**
* Creates rotation transformations around a center point along the Z axis.
* Example: center=[10,10,0], angle=180° → rotates 180° around Z axis through point [10,10,0]
* @param inputs Rotation around center with an Z axis information
* @returns array of transformations
* @group rotation
* @shortname center z
* @drawable false
*/
rotationCenterZ(inputs: Inputs.Transforms.RotationCenterDto): Base.TransformMatrixes {
return [
this.translation(-inputs.center[0], -inputs.center[1], -inputs.center[2]),
this.rotationZ(this.math.degToRad({ number: inputs.angle })),
this.translation(inputs.center[0], inputs.center[1], inputs.center[2]),
] as Base.TransformMatrixes;
}
/**
* Creates rotation transformations using yaw-pitch-roll (Euler angles) around a center point.
* Yaw → Y axis rotation, Pitch → X axis rotation, Roll → Z axis rotation.
* Example: center=[0,0,0], yaw=90°, pitch=0°, roll=0° → rotates 90° around Y axis
* @param inputs Yaw pitch roll rotation information
* @returns array of transformations
* @group rotation
* @shortname yaw pitch roll
* @drawable false
*/
rotationCenterYawPitchRoll(inputs: Inputs.Transforms.RotationCenterYawPitchRollDto): Base.TransformMatrixes {
return [
this.translation(-inputs.center[0], -inputs.center[1], -inputs.center[2]),
this.rotationYawPitchRoll(
this.math.degToRad({ number: inputs.yaw }),
this.math.degToRad({ number: inputs.pitch }),
this.math.degToRad({ number: inputs.roll })),
this.translation(inputs.center[0], inputs.center[1], inputs.center[2]),
] as Base.TransformMatrixes;
}
/**
* Creates non-uniform scale transformation around a center point (different scale per axis).
* Example: center=[5,5,5], scaleXyz=[2,1,0.5] → doubles X, keeps Y, halves Z around point [5,5,5]
* @param inputs Scale center xyz trnansformation
* @returns array of transformations
* @group scale
* @shortname center xyz
* @drawable false
*/
scaleCenterXYZ(inputs: Inputs.Transforms.ScaleCenterXYZDto): Base.TransformMatrixes {
return [
this.translation(-inputs.center[0], -inputs.center[1], -inputs.center[2]),
this.scaling(inputs.scaleXyz[0], inputs.scaleXyz[1], inputs.scaleXyz[2]),
this.translation(inputs.center[0], inputs.center[1], inputs.center[2]),
] as Base.TransformMatrixes;
}
/**
* Creates non-uniform scale transformation from origin (different scale per axis).
* Example: scaleXyz=[2,3,1] → doubles X, triples Y, keeps Z unchanged
* @param inputs Scale XYZ number array information
* @returns transformation
* @group scale
* @shortname xyz
* @drawable false
*/
scaleXYZ(inputs: Inputs.Transforms.ScaleXYZDto): Base.TransformMatrixes {
return [this.scaling(inputs.scaleXyz[0], inputs.scaleXyz[1], inputs.scaleXyz[2])] as Base.TransformMatrixes;
}
/**
* Creates directional stretch transformation that scales along a specific direction from a center point.
* Points move only along the direction vector; perpendicular plane remains unchanged.
* Example: center=[0,0,0], direction=[1,0,0], scale=2 → stretches 2× along X axis only
* @param inputs Defines the center, direction, and scale factor for the stretch.
* @returns Array of transformations: [Translate To Origin, Stretch, Translate Back].
* @group scale
* @shortname stretch dir center
* @drawable false
*/
stretchDirFromCenter(inputs: Inputs.Transforms.StretchDirCenterDto): Base.TransformMatrixes {
return [
this.translation(-inputs.center[0], -inputs.center[1], -inputs.center[2]),
this.stretchDirection(inputs.direction, inputs.scale),
this.translation(inputs.center[0], inputs.center[1], inputs.center[2]),
] as Base.TransformMatrixes;
}
/**
* Creates uniform scale transformation from origin (same scale on all axes).
* Example: scale=2 → doubles size in all directions (X, Y, Z)
* @param inputs Scale Dto
* @returns transformation
* @group scale
* @shortname uniform
* @drawable false
*/
uniformScale(inputs: Inputs.Transforms.UniformScaleDto): Base.TransformMatrixes {
return [this.scaling(inputs.scale, inputs.scale, inputs.scale)] as Base.TransformMatrixes;
}
/**
* Creates uniform scale transformation around a center point (same scale on all axes).
* Example: center=[5,5,5], scale=0.5 → halves size in all directions around point [5,5,5]
* @param inputs Scale Dto with center point information
* @returns array of transformations
* @group scale
* @shortname uniform from center
* @drawable false
*/
uniformScaleFromCenter(inputs: Inputs.Transforms.UniformScaleFromCenterDto): Base.TransformMatrixes {
return [
this.translation(-inputs.center[0], -inputs.center[1], -inputs.center[2]),
this.scaling(inputs.scale, inputs.scale, inputs.scale),
this.translation(inputs.center[0], inputs.center[1], inputs.center[2]),
] as Base.TransformMatrixes;
}
/**
* Creates translation transformation (moves objects in space).
* Example: translation=[10,5,0] → moves object 10 units in X, 5 in Y, 0 in Z
* @param inputs Translation information
* @returns transformation
* @group translation
* @shortname xyz
* @drawable false
*/
translationXYZ(inputs: Inputs.Transforms.TranslationXYZDto): Base.TransformMatrixes {
return [this.translation(inputs.translation[0], inputs.translation[1], inputs.translation[2])] as Base.TransformMatrixes;
}
/**
* Creates multiple translation transformations (batch move operations).
* Example: translations=[[1,0,0], [0,2,0]] → generates two transforms: move +X, move +Y
* @param inputs Translation information
* @returns transformation
* @group translations
* @shortname xyz
* @drawable false
*/
translationsXYZ(inputs: Inputs.Transforms.TranslationsXYZDto): Base.TransformMatrixes[] {
return inputs.translations.map(translation => [this.translation(translation[0], translation[1], translation[2])]) as Base.TransformMatrixes[];
}
/**
* Creates identity transformation matrix (no transformation - leaves objects unchanged).
* Returns 4×4 matrix: [1,0,0,0, 0,1,0,0, 0,0,1,0, 0,0,0,1]
* @returns transformation
* @group identity
* @shortname identity
* @drawable false
*/
identity(): Base.TransformMatrix {
return [1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0];
}
private translation(x: number, y: number, z: number) {
return [1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, x, y, z, 1.0];
}
private scaling(x: number, y: number, z: number) {
return [x, 0.0, 0.0, 0.0, 0.0, y, 0.0, 0.0, 0.0, 0.0, z, 0.0, 0.0, 0.0, 0.0, 1.0];
}
private rotationAxis(axis: Base.Vector3, angle: number) {
const s = Math.sin(-angle);
const c = Math.cos(-angle);
const c1 = 1 - c;
const a = this.vector.normalized({ vector: axis });
const x = a[0];
const y = a[1];
const z = a[2];
const m = this.identity();
m[0] = x * x * c1 + c;
m[1] = x * y * c1 - z * s;
m[2] = x * z * c1 + y * s;
m[3] = 0.0;
m[4] = y * x * c1 + z * s;
m[5] = y * y * c1 + c;
m[6] = y * z * c1 - x * s;
m[7] = 0.0;
m[8] = z * x * c1 - y * s;
m[9] = z * y * c1 + x * s;
m[10] = z * z * c1 + c;
m[11] = 0.0;
m[12] = 0.0;
m[13] = 0.0;
m[14] = 0.0;
m[15] = 1.0;
return m;
}
private rotationX(angle: number) {
const s = Math.sin(angle);
const c = Math.cos(angle);
return [1.0, 0.0, 0.0, 0.0, 0.0, c, s, 0.0, 0.0, -s, c, 0.0, 0.0, 0.0, 0.0, 1.0];
}
private rotationY(angle: number) {
const s = Math.sin(angle);
const c = Math.cos(angle);
return [c, 0.0, -s, 0.0, 0.0, 1.0, 0.0, 0.0, s, 0.0, c, 0.0, 0.0, 0.0, 0.0, 1.0];
}
private rotationZ(angle: number) {
const s = Math.sin(angle);
const c = Math.cos(angle);
return [c, s, 0.0, 0.0, -s, c, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0];
}
private rotationYawPitchRoll(yaw: number, pitch: number, roll: number) {
const halfRoll = roll * 0.5;
const halfPitch = pitch * 0.5;
const halfYaw = yaw * 0.5;
const sinRoll = Math.sin(halfRoll);
const cosRoll = Math.cos(halfRoll);
const sinPitch = Math.sin(halfPitch);
const cosPitch = Math.cos(halfPitch);
const sinYaw = Math.sin(halfYaw);
const cosYaw = Math.cos(halfYaw);
const x = cosYaw * sinPitch * cosRoll + sinYaw * cosPitch * sinRoll;
const y = sinYaw * cosPitch * cosRoll - cosYaw * sinPitch * sinRoll;
const z = cosYaw * cosPitch * sinRoll - sinYaw * sinPitch * cosRoll;
const w = cosYaw * cosPitch * cosRoll + sinYaw * sinPitch * sinRoll;
return this.rotationMatrixFromQuat(x, y, z, w);
}
private rotationMatrixFromQuat(x: number, y: number, z: number, w: number) {
const xx = x * x;
const yy = y * y;
const zz = z * z;
const xy = x * y;
const zw = z * w;
const zx = z * x;
const yw = y * w;
const yz = y * z;
const xw = x * w;
const m = this.identity();
m[0] = 1.0 - 2.0 * (yy + zz);
m[1] = 2.0 * (xy + zw);
m[2] = 2.0 * (zx - yw);
m[3] = 0.0;
m[4] = 2.0 * (xy - zw);
m[5] = 1.0 - 2.0 * (zz + xx);
m[6] = 2.0 * (yz + xw);
m[7] = 0.0;
m[8] = 2.0 * (zx + yw);
m[9] = 2.0 * (yz - xw);
m[10] = 1.0 - 2.0 * (yy + xx);
m[11] = 0.0;
m[12] = 0.0;
m[13] = 0.0;
m[14] = 0.0;
m[15] = 1.0;
return m;
}
/**
* Creates a 4x4 matrix that scales along a given direction vector.
* @param direction The direction vector (will be normalized).
* @param scale The scale factor along the direction.
* @returns A 4x4 column-major transformation matrix.
*/
private stretchDirection(direction: Base.Vector3, scale: number): Base.TransformMatrix {
const d = this.vector.normalized({ vector: direction });
const [dx, dy, dz] = d;
// Handle potential zero vector after normalization (if input was zero)
Iif (isNaN(dx) || (dx === 0 && dy === 0 && dz === 0)) {
console.warn("Stretch direction vector is zero or invalid. Returning identity matrix.");
return this.identity();
}
const s = scale;
const sMinus1 = s - 1.0;
// Calculate elements of the 3x3 directional scaling part
const m11 = 1.0 + sMinus1 * dx * dx;
const m12 = sMinus1 * dx * dy;
const m13 = sMinus1 * dx * dz;
// m14 = 0
const m21 = sMinus1 * dy * dx;
const m22 = 1.0 + sMinus1 * dy * dy;
const m23 = sMinus1 * dy * dz;
// m24 = 0
const m31 = sMinus1 * dz * dx;
const m32 = sMinus1 * dz * dy;
const m33 = 1.0 + sMinus1 * dz * dz;
// m34 = 0
// m41, m42, m43 = 0, m44 = 1
// Assemble the 4x4 matrix in COLUMN-MAJOR order
const m: Base.TransformMatrix = [
m11, m21, m31, 0.0, // Column 1
m12, m22, m32, 0.0, // Column 2
m13, m23, m33, 0.0, // Column 3
0.0, 0.0, 0.0, 1.0 // Column 4
];
return m;
}
}
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