Documentation Index
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Double3x3 is a 3×3 double-precision floating-point matrix in the Prowl.Vector namespace. It uses column-major storage — each column field (c0, c1, c2) is a Double3. The struct is marked [Serializable] and is frequently used for pure rotation/scale transforms, normal-vector transforms, and as the upper-left 3×3 block of a Double4x4.
Declaration
[System.Serializable]
public partial struct Double3x3 : System.IEquatable<Double3x3>, IFormattable
Fields
| Field | Type | Description |
|---|
c0 | Double3 | Column 0 — stores m00, m10, m20 (X-basis / first column). |
c1 | Double3 | Column 1 — stores m01, m11, m21 (Y-basis / second column). |
c2 | Double3 | Column 2 — stores m02, m12, m22 (Z-basis / third column, also aliased as Translation). |
this[row, col] resolves to this[col][row].
Static Constants
| Constant | Value | Description |
|---|
Double3x3.Identity | Diagonal (1, 1, 1) | The multiplicative identity. |
Double3x3.Zero | All zeros | A zeroed matrix. |
Double3x3 m = Double3x3.Identity;
Constructors
From three column vectors
public Double3x3(Double3 col0, Double3 col1, Double3 col2)
From nine scalar values (row-major argument order)
public Double3x3(
double m00, double m01, double m02,
double m10, double m11, double m12,
double m20, double m21, double m22)
Broadcast scalar
public Double3x3(double v)
v.
Widening from Float3x3
public Double3x3(Float3x3 m)
(Double3x3)float3x3 also available.
public Double3x3(Double4x4 d4x4)
c0.XYZ, c1.XYZ, c2.XYZ).
Properties
Translation
public Double3 Translation { get; set; }
c2. In an affine 2D homogeneous context this column holds the translation; in a pure 3D rotation matrix the alias is a naming convention only.
Column indexer
public ref Double3 this[int index] // index in [0, 2]
ArgumentOutOfRangeException for out-of-range indices.
Element indexer
public double this[int row, int column] { get; set; } // each in [0, 2]
this[column][row].
Instance Methods
Row accessors
public Double3 GetRow0();
public Double3 GetRow1();
public Double3 GetRow2();
public void SetRow0(Double3 value);
public void SetRow1(Double3 value);
public void SetRow2(Double3 value);
Invert (instance)
public Double3x3 Invert()
NaN-filled matrix if singular.
Static Factory Methods
FromQuaternion
public static Double3x3 FromQuaternion(Quaternion q)
FromAxisAngle
public static Double3x3 FromAxisAngle(Double3 axis, double angle)
axis must be normalised; angle is in radians.
RotateX / RotateY / RotateZ
public static Double3x3 RotateX(double angle)
public static Double3x3 RotateY(double angle)
public static Double3x3 RotateZ(double angle)
angle is in radians. Computes sin/cos once and inserts them into the canonical locations.
Scale
public static Double3x3 Scale(double s) // uniform
public static Double3x3 Scale(double x, double y, double z) // non-uniform
public static Double3x3 Scale(Double3 v) // from vector
s on all three diagonal entries; the non-uniform overloads allow per-axis values.
CreateLookRotation
public static Double3x3 CreateLookRotation(Double3 forward, Double3 up)
forward direction and a reference up vector. Returns Identity if either input is degenerate or if forward and up are collinear.
Basis construction:
zAxis = normalize(forward)xAxis = normalize(cross(up, zAxis))yAxis = cross(zAxis, xAxis)
Transpose
public static Double3x3 Transpose(Double3x3 m)
m. For orthonormal rotation matrices, this is equivalent to the inverse.
Determinant
public static double Determinant(Double3x3 m)
a · (b × c)).
Invert (static)
public static bool Invert(Double3x3 matrix, out Double3x3 result)
true on success. If |det| < double.Epsilon, writes NaN to result and returns false.
public static Double2 TransformPoint(Double2 point, Double3x3 matrix)
point to homogeneous coordinates (x, y, 1), multiplies by the 3×3 matrix, then divides by z to recover the 2D result.
// 2-D normal (delegates to Double2x2.TransformNormal via upper-left 2x2)
public static Double2 TransformNormal(Double2 normal, Double3x3 matrix)
// 3-D normal (inverse-transpose method)
public static Double3 TransformNormal(Double3 normal, Double3x3 matrix)
(M⁻¹)ᵀ · normal then normalises; the 2D overload extracts the upper-left Double2x2 and delegates.
Operators
| Operator | Signature | Notes |
|---|
* | Double3x3 * Double3x3 → Double3x3 | Matrix product. A * B applies B first, then A. |
* | Double3x3 * Double3 → Double3 | Matrix–vector product. |
== | Double3x3 == Double3x3 → bool | Component-wise equality. |
!= | Double3x3 != Double3x3 → bool | Logical negation of ==. |
Explicit casts
explicit operator Double3x3(Float3x3 m) // widening: float → double
explicit operator Float3x3(Double3x3 m) // narrowing (on Float3x3 side)
Additional Methods
ToArray
public double[] ToArray()
double[9] in row-major order ([row * 3 + col]).
ToString
public override string ToString()
public string ToString(string format)
public string ToString(string format, IFormatProvider formatProvider)
Double3x3(1, 0, 0, 0, 1, 0, 0, 0, 1).
Code Example
using Prowl.Vector;
// 1. Rotation from a unit quaternion
var quat = Quaternion.FromEuler(17.2f, 5.7f, 0.0f);
Double3x3 rot = Double3x3.FromQuaternion(quat);
// 2. Rotation around an arbitrary axis
var axis = Double3.Normalize(new Double3(1.0, 1.0, 0.0));
Double3x3 axisRot = Double3x3.FromAxisAngle(axis, Maths.PI / 4.0); // 45°
// 3. Elementary rotations
Double3x3 rx = Double3x3.RotateX(Maths.PI / 6.0); // 30° around X
Double3x3 ry = Double3x3.RotateY(Maths.PI / 4.0); // 45° around Y
Double3x3 combined = rx * ry;
// 4. Non-uniform scale
Double3x3 scale = Double3x3.Scale(2.0, 1.0, 0.5);
// 5. Transform a normal through a scaled matrix
Double3 normal = Double3.UnitY;
Double3 tNormal = Double3x3.TransformNormal(normal, scale); // inverse-transpose applied
// 6. View rotation (look-at, rotation part only)
Double3x3 lookRot = Double3x3.CreateLookRotation(
forward: Double3.Normalize(new Double3(0.0, -1.0, 1.0)),
up: Double3.UnitY);
// 7. Extract from a 4x4 matrix
Double4x4 trs = Double4x4.CreateTRS(Double3.Zero, quat, Double3.One);
Double3x3 upperLeft = new Double3x3(trs);
// 8. Inverse and determinant
bool ok = Double3x3.Invert(combined, out Double3x3 inv);
double det = Double3x3.Determinant(combined);