gl3n.linalg

gl3n.linalg

Discussion

Special thanks to:

  • Tomasz Stachowiak (h3r3tic): allowed me to use parts of omg.
  • Jakob Øvrum (jA_cOp): improved the code a lot!
  • Florian Boesch (__doc__): helps me to understand opengl/complex maths better, see: http://codeflow.org/.
  • #D on freenode: answered general questions about D.

Authors

David Herberth

License

MIT

Note: All methods marked with pure are weakly pure since, they all access an instance member. All static methods are strongly pure.

  • Vector

    Declaration

    struct Vector(type, int dimension_);

    Base template for all vector-types.

    Parameters

    type

    all values get stored as this type

    dimension

    specifies the dimension of the vector, can be 1, 2, 3 or 4

    Examples

    1. alias Vector!(int, 3) vec3i; alias Vector!(float, 4) vec4; alias Vector!(real, 2) vec2r;

    • vt

      Declaration

      alias vt = type;

      Holds the internal type of the vector.

    • dimension

      Declaration

      static const int dimension;

      Holds the dimension of the vector.

    • vector

      Declaration

      vt[dimension] vector;

      Holds all coordinates, length conforms dimension.

    • value_ptr

      Declaration

      const @property auto value_ptr();

      Returns a pointer to the coordinates.

    • as_string

      Declaration

      @property string as_string();
      alias toString = as_string;

      Returns the current vector formatted as string, useful for printing the vector.

    • get_

      Declaration

      inout @property ref inout(vt) get_(char coord)();

    • x

      Declaration

      alias x = get_!'x';
      alias u = x;
      alias s = x;
      alias r = x;
      alias y = get_!'y';
      alias v = y;
      alias t = y;
      alias g = y;
      alias z = get_!'z';
      alias b = z;
      alias p = z;
      alias w = get_!'w';
      alias a = w;
      alias q = w;

      static properties to access the values.

    • e1

      Declaration

      enum Vector e1;
      enum Vector e2;

      canonical basis for Euclidian space

    • this

      Declaration

      this(Args...)(Args args);
      this(T)(T vec) if (is_vector!T && is(T.vt : vt) && (T.dimension >= dimension));
      this()(vt value);

      Constructs the vector. If a single value is passed the vector, the vector will be cleared with this value. If a vector with a higher dimension is passed the vector will hold the first values up to its dimension. If mixed types are passed they will be joined together (allowed types: vector, static array, vt).

      Examples

      1. vec4 v4 = vec4(1.0f, vec2(2.0f, 3.0f), 4.0f); vec3 v3 = vec3(v4); // v3 = vec3(1.0f, 2.0f, 3.0f); vec2 v2 = v3.xy; // swizzling returns a static array. vec3 v3_2 = vec3(1.0f); // vec3 v3_2 = vec3(1.0f, 1.0f, 1.0f);

    • isFinite

      Declaration

      const @property bool isFinite();

      Returns true if all values are not nan and finite, otherwise false.

    • clear

      Declaration

      void clear(vt value);

      Sets all values of the vector to value.

    • update

      Declaration

      void update(Vector!(vt, dimension) other);

      Updates the vector with the values from other.

    • opDispatch

      Declaration

      const @property Vector!(vt, s.length) opDispatch(string s)();

      Implements dynamic swizzling.

      Return Value

      a Vector

    • magnitude_squared

      Declaration

      const @property real magnitude_squared();

      Returns the squared magnitude of the vector.

    • magnitude

      Declaration

      const @property real magnitude();
      alias length_squared = magnitude_squared;
      alias length = magnitude;

      Returns the magnitude of the vector.

    • normalize

      Declaration

      void normalize();

      Normalizes the vector.

    • normalized

      Declaration

      const @property Vector normalized();

      Returns a normalized copy of the current vector.

  • dot

    Declaration

    pure nothrow @safe T.vt dot(T)(const T veca, const T vecb) if (is_vector!T);

    Calculates the product between two vectors.

  • cross

    Declaration

    pure nothrow @safe T cross(T)(const T veca, const T vecb) if (is_vector!T && (T.dimension == 3));

    Calculates the cross product of two 3-dimensional vectors.

  • distance

    Declaration

    pure nothrow @safe T.vt distance(T)(const T veca, const T vecb) if (is_vector!T);

    Calculates the distance between two vectors.

  • reflect

    Declaration

    pure nothrow @safe T reflect(T)(const T vec, const T norm) if (is_vector!T);

    reflect a vector using a surface normal

  • vec2

    Declaration

    alias vec2 = Vector!(float, 2).Vector;
    alias vec3 = Vector!(float, 3).Vector;
    alias vec4 = Vector!(float, 4).Vector;
    alias vec2d = Vector!(double, 2).Vector;
    alias vec3d = Vector!(double, 3).Vector;
    alias vec4d = Vector!(double, 4).Vector;
    alias vec2i = Vector!(int, 2).Vector;
    alias vec3i = Vector!(int, 3).Vector;
    alias vec4i = Vector!(int, 4).Vector;

    Pre-defined vector types, the number represents the dimension and the last letter the type (none = float, d = double, i = int).

  • Matrix

    Declaration

    struct Matrix(type, int rows_, int cols_) if (rows_ > 0 && (cols_ > 0));

    Base template for all matrix-types.

    Parameters

    type

    all values get stored as this type

    rows_

    rows of the matrix

    cols_

    columns of the matrix

    Examples

    1. alias Matrix!(float, 4, 4) mat4; alias Matrix!(double, 3, 4) mat34d; alias Matrix!(real, 2, 2) mat2r;

    • mt

      Declaration

      alias mt = type;

      Holds the internal type of the matrix;

    • rows

      Declaration

      static const int rows;

      Holds the number of rows;

    • cols

      Declaration

      static const int cols;

      Holds the number of columns;

    • matrix

      Declaration

      mt[cols][rows] matrix;

      Holds the matrix row-major in memory.

    • value_ptr

      Declaration

      const @property auto value_ptr();

      Returns the pointer to the stored values as OpenGL requires it. Note this will return a pointer to a row-major matrix, this means you've to set the transpose argument to GL_TRUE when passing it to OpenGL.

      Examples

      1. // 3rd argument = GL_TRUE glUniformMatrix4fv(programs.main.model, 1, GL_TRUE, mat4.translation(-0.5f, -0.5f, 1.0f).value_ptr);

    • as_string

      Declaration

      @property string as_string();
      alias toString = as_string;

      Returns the current matrix formatted as flat string.

    • as_pretty_string

      Declaration

      @property string as_pretty_string();
      alias toPrettyString = as_pretty_string;

      Returns the current matrix as pretty formatted string.

    • this

      Declaration

      this(Args...)(Args args);
      this(T)(T mat) if (is_matrix!T && (T.cols >= cols) && (T.rows >= rows));
      this(T)(T mat) if (is_matrix!T && (T.cols < cols) && (T.rows < rows));
      this()(mt value);

      Constructs the matrix: If a single value is passed, the matrix will be cleared with this value (each column in each row will contain this value). If a matrix with more rows and columns is passed, the matrix will be the upper left nxm matrix. If a matrix with less rows and columns is passed, the passed matrix will be stored in the upper left of an identity matrix. It's also allowed to pass vectors and scalars at a time, but the vectors dimension must match the number of columns and align correctly.

      Examples

      1. mat2 m2 = mat2(0.0f); // mat2 m2 = mat2(0.0f, 0.0f, 0.0f, 0.0f); mat3 m3 = mat3(m2); // mat3 m3 = mat3(0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 1.0f); mat3 m3_2 = mat3(vec3(1.0f, 2.0f, 3.0f), 4.0f, 5.0f, 6.0f, vec3(7.0f, 8.0f, 9.0f)); mat4 m4 = mat4.identity; // just an identity matrix mat3 m3_3 = mat3(m4); // mat3 m3_3 = mat3.identity

    • isFinite

      Declaration

      const @property bool isFinite();

      Returns true if all values are not nan and finite, otherwise false.

    • clear

      Declaration

      void clear(mt value);

      Sets all values of the matrix to value (each column in each row will contain this value).

    • make_identity

      Declaration

      void make_identity();

      Makes the current matrix an identity matrix.

    • identity

      Declaration

      static @property Matrix identity();

      Returns a identity matrix.

    • transpose

      Declaration

      void transpose();

      Transposes the current matrix;

    • transposed

      Declaration

      const @property Matrix!(mt, cols, rows) transposed();

      Returns a transposed copy of the matrix.

    • translation

      Declaration

      static Matrix translation(mt x, mt y, mt z);
      static Matrix translation(Vector!(mt, 3) v);

      Returns a translation matrix (3x3 and 4x4 matrices).

    • translate

      Declaration

      Matrix translate(mt x, mt y, mt z);
      Matrix translate(Vector!(mt, 3) v);

      Applys a translation on the current matrix and returns this (3x3 and 4x4 matrices).

    • scaling

      Declaration

      static Matrix scaling(mt x, mt y, mt z);

      Returns a scaling matrix (3x3 and 4x4 matrices);

    • scale

      Declaration

      Matrix scale(mt x, mt y, mt z);

      Applys a scale to the current matrix and returns this (3x3 and 4x4 matrices).

    • rotation

      Declaration

      static Matrix rotation(real alpha, Vector!(mt, 3) axis);
      static Matrix rotation(real alpha, mt x, mt y, mt z);

      Returns an identity matrix with an applied rotate_axis around an arbitrary axis (nxn matrices, n >= 3).

    • xrotation

      Declaration

      static Matrix xrotation(real alpha);

      Returns an identity matrix with an applied rotation around the x-axis (nxn matrices, n >= 3).

    • yrotation

      Declaration

      static Matrix yrotation(real alpha);

      Returns an identity matrix with an applied rotation around the y-axis (nxn matrices, n >= 3).

    • zrotation

      Declaration

      static Matrix zrotation(real alpha);

      Returns an identity matrix with an applied rotation around the z-axis (nxn matrices, n >= 3).

    • rotatex

      Declaration

      Matrix rotatex(real alpha);

      Rotates the current matrix around the x-axis and returns this (nxn matrices, n >= 3).

    • rotatey

      Declaration

      Matrix rotatey(real alpha);

      Rotates the current matrix around the y-axis and returns this (nxn matrices, n >= 3).

    • rotatez

      Declaration

      Matrix rotatez(real alpha);

      Rotates the current matrix around the z-axis and returns this (nxn matrices, n >= 3).

    • set_translation

      Declaration

      void set_translation(mt[] values...);

      Sets the translation of the matrix (nxn matrices, n >= 3).

    • set_translation

      Declaration

      void set_translation(Matrix mat);

      Copyies the translation from mat to the current matrix (nxn matrices, n >= 3).

    • get_translation

      Declaration

      Matrix get_translation();

      Returns an identity matrix with the current translation applied (nxn matrices, n >= 3)..

    • set_scale

      Declaration

      void set_scale(mt[] values...);

      Sets the scale of the matrix (nxn matrices, n >= 3).

    • set_scale

      Declaration

      void set_scale(Matrix mat);

      Copyies the scale from mat to the current matrix (nxn matrices, n >= 3).

    • get_scale

      Declaration

      Matrix get_scale();

      Returns an identity matrix with the current scale applied (nxn matrices, n >= 3).

    • set_rotation

      Declaration

      void set_rotation(Matrix!(mt, 3, 3) rot);

      Copies rot into the upper left corner, the translation (nxn matrices, n >= 3).

    • get_rotation

      Declaration

      Matrix!(mt, 3, 3) get_rotation();

      Returns an identity matrix with the current rotation applied (nxn matrices, n >= 3).

    • inverse

      Declaration

      const @property Matrix inverse();

      Returns an inverted copy of the current matrix (nxn matrices, 2 >= n <= 4).

    • invert

      Declaration

      void invert();

      Inverts the current matrix (nxn matrices, 2 >= n <= 4).

  • mat2

    Declaration

    alias mat2 = Matrix!(float, 2, 2).Matrix;

    Pre-defined matrix types, the first number represents the number of rows and the second the number of columns, if there's just one it's a nxn matrix. All of these matrices are floating-point matrices.

  • Quaternion

    Declaration

    struct Quaternion(type);

    Base template for all quaternion-types.

    Parameters

    type

    all values get stored as this type

    • qt

      Declaration

      alias qt = type;

      Holds the internal type of the quaternion.

    • quaternion

      Declaration

      qt[4] quaternion;

      Holds the w, x, y and z coordinates.

    • value_ptr

      Declaration

      const @property auto value_ptr();

      Returns a pointer to the quaternion in memory, it starts with the w coordinate.

    • as_string

      Declaration

      @property string as_string();

      Returns the current vector formatted as string, useful for printing the quaternion.

    • w

      Declaration

      alias w = get_!'w';
      alias x = get_!'x';
      alias y = get_!'y';
      alias z = get_!'z';

      static properties to access the values.

    • this

      Declaration

      this(qt w_, qt x_, qt y_, qt z_);
      this(qt w_, Vector!(qt, 3) vec);
      this(Vector!(qt, 4) vec);

      Constructs the quaternion. Takes a 4-dimensional vector, where vector.x = the quaternions w coordinate, or a w coordinate of type qt and a 3-dimensional vector representing the imaginary part, or 4 values of type qt.

    • isFinite

      Declaration

      const @property bool isFinite();

      Returns true if all values are not nan and finite, otherwise false.

    • magnitude_squared

      Declaration

      const @property real magnitude_squared();

      Returns the squared magnitude of the quaternion.

    • magnitude

      Declaration

      const @property real magnitude();

      Returns the magnitude of the quaternion.

    • identity

      Declaration

      static @property Quaternion identity();

      Returns an identity quaternion (w=1, x=0, y=0, z=0).

    • make_identity

      Declaration

      void make_identity();

      Makes the current quaternion an identity quaternion.

    • invert

      Declaration

      void invert();
      alias conjugate = invert;

      Inverts the quaternion.

    • inverse

      Declaration

      const @property Quaternion inverse();
      alias conjugated = inverse;

      Returns an inverted copy of the current quaternion.

    • from_matrix

      Declaration

      static Quaternion from_matrix(Matrix!(qt, 3, 3) matrix);

      Creates a quaternion from a 3x3 matrix.

      Parameters

      Matrix!(qt, 3, 3) matrix

      3x3 matrix (rotation)

      Return Value

      A quaternion representing the rotation (3x3 matrix)

    • to_matrix

      Declaration

      const Matrix!(qt, rows, cols) to_matrix(int rows, int cols)() if (rows >= 3 && (cols >= 3));

      Returns the quaternion as matrix.

      Parameters

      rows

      number of rows of the resulting matrix (min 3)

      cols

      number of columns of the resulting matrix (min 3)

    • to_axis_angle

      Declaration

      vec3 to_axis_angle();

      Returns the quaternion as a vec3 (axis / angle representation).

    • normalize

      Declaration

      void normalize();

      Normalizes the current quaternion.

    • normalized

      Declaration

      const Quaternion normalized();

      Returns a normalized copy of the current quaternion.

    • yaw

      Declaration

      const @property real yaw();

      Returns the yaw.

    • pitch

      Declaration

      const @property real pitch();

      Returns the pitch.

    • roll

      Declaration

      const @property real roll();

      Returns the roll.

    • xrotation

      Declaration

      static Quaternion xrotation(real alpha);

      Returns a quaternion with applied rotation around the x-axis.

    • yrotation

      Declaration

      static Quaternion yrotation(real alpha);

      Returns a quaternion with applied rotation around the y-axis.

    • zrotation

      Declaration

      static Quaternion zrotation(real alpha);

      Returns a quaternion with applied rotation around the z-axis.

    • axis_rotation

      Declaration

      static Quaternion axis_rotation(real alpha, Vector!(qt, 3) axis);

      Returns a quaternion with applied rotation around an axis.

    • euler_rotation

      Declaration

      static Quaternion euler_rotation(real roll, real pitch, real yaw);

      Creates a quaternion from an euler rotation.

    • rotatex

      Declaration

      Quaternion rotatex(real alpha);

      Rotates the current quaternion around the x-axis and returns this.

    • rotatey

      Declaration

      Quaternion rotatey(real alpha);

      Rotates the current quaternion around the y-axis and returns this.

    • rotatez

      Declaration

      Quaternion rotatez(real alpha);

      Rotates the current quaternion around the z-axis and returns this.

    • rotate_axis

      Declaration

      Quaternion rotate_axis(real alpha, Vector!(qt, 3) axis);

      Rotates the current quaternion around an axis and returns this.

    • rotate_euler

      Declaration

      Quaternion rotate_euler(real heading, real attitude, real bank);

      Applies an euler rotation to the current quaternion and returns this.

  • quat

    Declaration

    alias quat = Quaternion!float.Quaternion;

    Pre-defined quaternion of type float.