The goal of this library is to provide the mathematical objects commonly used in games:

• all values have 32 bit floating point type unless otherwise noted
• vec2, vec3, vec4 (2,3 and 4 dimension vectors)
• mat4 (4x4 matrix)
• aabb2 (2D axis-aligned bounding box)
• aabb3 (3D axis-aligned bounding box)
• color (red, green, blue, alpha values)
• floatarray (array of floating point values)

The library is compiled to a 'sgsxgmath' shared library so it can be included this way (assuming that, on Linux and similar systems, LD_LIBRARY_PATH is set correctly):

include "sgsxgmath";

iIt is extremely important that only one instance of this library is loaded in the application for constant sharing to enable object interface recognition.

Objects:

• vec2
• vec3
• vec4
• aabb2
• aabb3
• color
• mat4
• floatarray

Functions:

• vec2 - create a vec2 object
• vec2_dot - return dot product of two 2D vectors
• vec3 - create a vec3 object
• vec3_dot - return dot product of two 3D vectors
• vec3_cross - return cross product of two 3D vectors
• vec4 - create a vec4 object
• vec4_dot - return dot product of two 4D vectors
• aabb2 - create a 2D AABB from 4 real values
• aabb2v - create a 2D AABB from 2 2D vectors
• aabb2_intersect - intersect two 2D AABB values
• aabb3 - create a 3D AABB from 6 real values
• aabb3v - create a 3D AABB from 2 3D vectors
• aabb3_intersect - intersect two 3D AABB values
• color
• mat4
• floatarray - create floatarray from array/list of int/real values
• floatarray_buffer - create 0-initialized floatarray
• vec2array - create floatarray from array/list of int/real/vec2 values
• vec3array - create floatarray from array/list of int/real/vec3 values
• vec4array - create floatarray from array/list of int/real/vec4 values
• floatarray_from_*_buffer - create floatarray from byte buffer

• methods
  • rotate - return vector, rotated by specified angle
• read-only properties
  • [real] length
  • [real] length_squared
  • [vec2] normalized - return a vector with length = 1 if possible, length = 0 if too short
  • [vec2] perp - returns vec2(-y,x) - 90 degree clockwise vector
  • [vec2] perp2 - returns vec2(y,-x) - 90 degree counter-clockwise vector
  • [int] size - returns 2 - the number of components in this vector
• read/write properties
  • [real] x
  • [real] y
  • [real] angle
• overloaded operators
  • + - adds two vec2/real values
  • - - subtracts two vec2/real values
  • * - multiplies two vec2/real values
  • / - divides two vec2/real values
  • % - returns modulo of two vec2/real values
  • comparison between vec2 values: first by X, then by Y
  • unary - - returns negated vec2
• other features:
  • cloning support
  • serialization support
  • GC-safe
  • indexing support for indices 0 - 1: returns/sets the specified subvalue
  • tostring, dump = "vec2(<x>;<y>)"

vec2.rotate( real angle )

return vec2, rotated by angle in radians

vec2( real x[, real y ])

create a vec2 value from 1 - 2 real values

• if only one argument is given, it is used for both x and y

vec2_dot( vec2 v1, vec2 v2 )

return the dot product of both vectors

• returns v1.x v2.x + v1.y v2.y

• read-only properties
  • [real] length
  • [real] length_squared
  • [vec3] normalized - return a vector with length = 1 if possible, length = 0 if too short
  • [int] size - returns 3 - the number of components in this vector
• read/write properties
  • [real] x
  • [real] y
  • [real] z
• overloaded operators
  • + - adds two vec3/real values
  • - - subtracts two vec3/real values
  • * - multiplies two vec3/real values
  • / - divides two vec3/real values
  • % - returns modulo of two vec3/real values
  • comparison between vec3 values: first by X, then by Y, then by Z
  • unary - - returns negated vec3
• other features:
  • cloning support
  • serialization support
  • GC-safe
  • indexing support for indices 0 - 2: returns/sets the specified subvalue
  • tostring, dump = "vec3(<x>;<y>;<z>)"

vec3( real x[, real y[, real z ]])

create a vec3 value from 1 or 3 real values

• if only one argument is given, it is used for x, y and z

vec3_dot( vec3 v1, vec3 v2 )

return the dot product of both vectors

• returns v1.x v2.x + v1.y v2.y + v1.z * v2.z

vec3_cross( vec3 v1, vec3 v2 )

return the cross product of both vectors

• returns vec3( v1.y v2.z - v1.z v2.y, v1.z v2.x - v1.x v2.z, v1.x v2.y - v1.y v2.x )

• read-only properties
  • [real] length
  • [real] length_squared
  • [vec4] normalized - return a vector with length = 1 if possible, length = 0 if too short
  • [int] size - returns 4 - the number of components in this vector
• read/write properties
  • [real] x
  • [real] y
  • [real] z
  • [real] w
• overloaded operators
  • + - adds two vec4/real values
  • - - subtracts two vec4/real values
  • * - multiplies two vec4/real values
  • / - divides two vec4/real values
  • % - returns modulo of two vec4/real values
  • comparison between vec4 values: first by X, then by Y, then by Z, then by W
  • unary - - returns negated vec4
• other features:
  • cloning support
  • serialization support
  • GC-safe
  • indexing support for indices 0 - 3: returns/sets the specified subvalue
  • tostring, dump = "vec4(<x>;<y>;<z>;<w>)"

vec4( real x[, real y[, real z[, real w ]]])

create a vec4 value from 1, 2 or 4 real values

• if only one argument is given, it is used for x, y, z and w
• if two arguments are given, use argument 1 for x, y and z ; argument 2 for w

vec4_dot( vec4 v1, vec4 v2 )

return the dot product of both vectors

• returns v1.x v2.x + v1.y v2.y + v1.z v2.z + v1.w v2.w

In this object, assume 1 = min and 2 = max.

• methods
  • expand - include other vec2/aabb2 items in current AABB
• read-only properties
  • [real] width -- x2 - x1
  • [real] height -- y2 - y1
  • [vec2] center -- (p1 + p2) / 2
  • [real] area -- width * height
  • [bool] valid -- returns if x1 <= x2 and y1 <= y2
• read/write properties
  • [real] x1
  • [real] y1
  • [real] x2
  • [real] y2
  • [vec2] p1
  • [vec2] p2
• overloaded operators
  • comparison between aabb2 values: first by X1, then by Y1, then by X2, then by Y2
• other features:
  • cloning support
  • serialization support
  • GC-safe
  • tostring, dump = "aabb2(<x1>;<y1> - <x2>;<y2>)"

aabb2.expand( ... )

include other vec2/aabb2 items in current AABB

aabb2( real x1, real y1, real x2, real y2 )

create a 2D AABB object from 4 real values

aabb2v( vec2 p1, vec2 p2 )

create a 2D AABB object from 2 vec2 values

aabb2_intersect( aabb2 bb1, aabb2 bb2 )

check if two AABBs intersect

In this object, assume 1 = min and 2 = max.

• methods
  • expand - include other vec3/aabb3 items in current AABB
• read-only properties
  • [real] width -- x2 - x1
  • [real] height -- y2 - y1
  • [real] depth -- z2 - z1
  • [vec3] center -- (p1 + p2) / 2
  • [real] area -- width height depth
  • [bool] valid -- returns if x1 <= x2 and y1 <= y2 and z1 <= z2
• read/write properties
  • [real] x1
  • [real] y1
  • [real] z1
  • [real] x2
  • [real] y2
  • [real] z2
  • [vec3] p1
  • [vec3] p2
• overloaded operators
  • comparison between aabb3 values: first by X1, then by Y1, then by Z1, then by X2, then by Y2, then by Z2
• other features:
  • cloning support
  • serialization support
  • GC-safe
  • tostring, dump = "aabb3(<x1>;<y1>;<z1> - <x2>;<y2>;<z2>)"

aabb3.expand( ... )

include other vec3/aabb3 items in current AABB

aabb3( real x1, real y1, real x2, real y2 )

create a 2D AABB object from 4 real values

aabb3v( vec3 p1, vec3 p2 )

create a 2D AABB object from 2 vec3 values

aabb3_intersect( aabb3 bb1, aabb3 bb2 )

check if two AABBs intersect

• read-only properties
  • [int] size - returns 4 - the number of components in this vector
• read/write properties
  • [real] r
  • [real] g
  • [real] b
  • [real] a
• overloaded operators
  • + - adds two color/real values
  • - - subtracts two color/real values
  • * - multiplies two color/real values
  • / - divides two color/real values
  • % - returns modulo of two color/real values
  • comparison between color values: first by R, then by G, then by B, then by A
  • unary - - returns negated color
• other features:
  • cloning support
  • serialization support
  • GC-safe
  • indexing support for indices 0 - 3: returns/sets the specified subvalue
  • tostring, dump = "color(<r>;<g>;<b>;<a>)"

color( real r[, real g[, real b[, real a ]]])

create a color value from 1 to 4 real values

• if one argument is given, it is used for all components
• if two arguments are given, argument 1 is used for R, G and B, argument 2 is used for A
• if three arguments are given, they're used for R, G and B; 1 is the value of A

A quaternion

• methods
  • identity - set quaternion to identity
  • multiply - multiply this quaternion with another one
  • multiply_left - left-multiply this quaternion with another one
  • multiply2 - multiply two matrices into this one
  • invert - invert quaternion
  • invert_from - invert another quaternion into this one
  • rotateX - set or multiply a X-axis rotation quaternion
  • rotateY - set or multiply a Y-axis rotation quaternion
  • rotateZ - set or multiply a Z-axis rotation quaternion
  • rotate_axis_angle - set or multiply a custom axis rotation quaternion
  • rotate_axis_angle_v3 - set or multiply a custom axis rotation quaternion (vec3 argument)
  • transform - transform a 3D vector
• read-only properties
  • [real] length
  • [real] length_squared
  • [quat] normalized - return a quaternion with length = 1 if possible, length = 0 if too short
  • [int] size - returns 4 - the number of components in this vector
  • [mat3] mat3 - returns a 3x3 matrix, generated from this quaternion
  • [mat4] mat4 - returns a 4x4 matrix, generated from this quaternion
• read/write properties
  • [real] m[0-2][0-2]
• overloaded operators
  • comparison between subvalues: column-major subvalue order
• other features:
  • cloning support
  • serialization support
  • GC-safe
  • indexing support for indices 0 - 8: returns/sets the specified subvalue
  • tostring = "quat"
  • dump:

quat(<x>;<y>;<z>|<w>)

quat.identity()

set the quaternion to identity

quat.multiply( quat m )

multiply this quaternion and another quaternion, putting the other quaternion on the right side of multiplication

quat.multiply_left( quat m )

multiply this quaternion and another quaternion, putting the other quaternion on the left side of multiplication

quat.multiply2( quat m1, quat m2 )

multiply two matrices into this quaternion

quat.invert()

invert this quaternion into itself

quat.invert_from( quat m )

invert another quaternion into this quaternion

quat.rotateX( real a[, bool reset ])

generate a rotation quaternion (rotation around X axis) and multiply or set it to this quaternion

• if reset is true, the generated quaternion is directly set to this quaternion
  • otherwise, generated quaternion is right-multiplied to this quaternion
  • if current quaternion is an identity quaternion, reset has no effect

quat.rotateY( real a[, bool reset ])

generate a rotation quaternion (rotation around Y axis) and multiply or set it to this quaternion

• if reset is true, the generated quaternion is directly set to this quaternion
  • otherwise, generated quaternion is right-multiplied to this quaternion
  • if current quaternion is an identity quaternion, reset has no effect

quat.rotateZ( real a[, bool reset ])

generate a rotation quaternion (rotation around Z axis) and multiply or set it to this quaternion

• if reset is true, the generated quaternion is directly set to this quaternion
  • otherwise, generated quaternion is right-multiplied to this quaternion
  • if current quaternion is an identity quaternion, reset has no effect

quat.rotate_axis_angle( real x, real y, real z, real a[, bool reset ])

generate a rotation quaternion (rotation around specified axis) and multiply or set it to this quaternion

• if reset is true, the generated quaternion is directly set to this quaternion
  • otherwise, generated quaternion is right-multiplied to this quaternion
  • if current quaternion is an identity quaternion, reset has no effect

quat.rotate_axis_angle( vec3 v, real a[, bool reset ])

generate a rotation quaternion (rotation around specified axis) and multiply or set it to this quaternion

• if reset is true, the generated quaternion is directly set to this quaternion
  • otherwise, generated quaternion is right-multiplied to this quaternion
  • if current quaternion is an identity quaternion, reset has no effect

quat.transform( vec3 v )

multiply a 3D vector by this quaternion

quat( real v[4] )

create a quaternion from 4 real values

A 3x3 column-major matrix

• methods
  • identity - set matrix to identity
  • multiply - multiply this matrix with another one
  • multiply_left - left-multiply this matrix with another one
  • multiply2 - multiply two matrices into this one
  • transpose - transpose matrix
  • transpose_from - transpose another matrix into this one
  • invert - invert matrix
  • invert_from - invert another matrix into this one
  • rotateX - set or multiply a X-axis rotation matrix
  • rotateY - set or multiply a Y-axis rotation matrix
  • rotateZ - set or multiply a Z-axis rotation matrix
  • rotate_axis_angle - set or multiply a custom axis rotation matrix
  • rotate_axis_angle_v3 - set or multiply a custom axis rotation matrix (vec3 argument)
  • scale - set or multiply a scale matrix
  • scale_v3 - set or multiply a scale matrix (vec3 argument)
  • transform - transform a 3D vector
• read-only properties
  • [int] size - returns 9 - the number of components in this vector
  • [quat] quat - returns the quaternion version of this matrix
  • [mat4] mat4 - returns a 4x4 version of this matrix, expanded with identity matrix data
• read/write properties
  • [real] m[0-2][0-2]
• overloaded operators
  • comparison between subvalues: column-major subvalue order
• other features:
  • cloning support
  • serialization support
  • GC-safe
  • indexing support for indices 0 - 8: returns/sets the specified subvalue
  • tostring = "mat3"
  • dump:

mat3
(
	<m00> <m10> <m20>
	<m01> <m11> <m21>
	<m02> <m12> <m22>
)

mat3.identity()

set the matrix to identity

mat3.multiply( mat3 m )

multiply this matrix and another matrix, putting the other matrix on the right side of multiplication

mat3.multiply_left( mat3 m )

multiply this matrix and another matrix, putting the other matrix on the left side of multiplication

mat3.multiply2( mat3 m1, mat3 m2 )

multiply two matrices into this matrix

mat3.transpose()

transpose this matrix into itself

mat3.transpose_from( mat3 m )

transpose another matrix into this matrix

mat3.invert()

invert this matrix into itself, return if successful

mat3.invert_from( mat3 m )

invert another matrix into this matrix

mat3.rotateX( real a[, bool reset ])

generate a rotation matrix (rotation around X axis) and multiply or set it to this matrix

• if reset is true, the generated matrix is directly set to this matrix
  • otherwise, generated matrix is right-multiplied to this matrix
  • if current matrix is an identity matrix, reset has no effect

mat3.rotateY( real a[, bool reset ])

generate a rotation matrix (rotation around Y axis) and multiply or set it to this matrix

• if reset is true, the generated matrix is directly set to this matrix
  • otherwise, generated matrix is right-multiplied to this matrix
  • if current matrix is an identity matrix, reset has no effect

mat3.rotateZ( real a[, bool reset ])

generate a rotation matrix (rotation around Z axis) and multiply or set it to this matrix

• if reset is true, the generated matrix is directly set to this matrix
  • otherwise, generated matrix is right-multiplied to this matrix
  • if current matrix is an identity matrix, reset has no effect

mat3.rotate_axis_angle( real x, real y, real z, real a[, bool reset ])

generate a rotation matrix (rotation around specified axis) and multiply or set it to this matrix

• if reset is true, the generated matrix is directly set to this matrix
  • otherwise, generated matrix is right-multiplied to this matrix
  • if current matrix is an identity matrix, reset has no effect

mat3.rotate_axis_angle( vec3 v, real a[, bool reset ])

generate a rotation matrix (rotation around specified axis) and multiply or set it to this matrix

• if reset is true, the generated matrix is directly set to this matrix
  • otherwise, generated matrix is right-multiplied to this matrix
  • if current matrix is an identity matrix, reset has no effect

mat3.scale( real x, real y, real z[, bool reset ])

generate a scale matrix and multiply or set it to this matrix

• if reset is true, the generated matrix is directly set to this matrix
  • otherwise, generated matrix is right-multiplied to this matrix
  • if current matrix is an identity matrix, reset has no effect

mat3.scale_v3( vec3 v[, bool reset ])

generate a scale matrix and multiply or set it to this matrix

• if reset is true, the generated matrix is directly set to this matrix
  • otherwise, generated matrix is right-multiplied to this matrix
  • if current matrix is an identity matrix, reset has no effect

mat3.transform( vec3 v )

multiply a 3D vector by this matrix

mat3( mat3 m )

copy the matrix

mat3( vec3 row1, vec3 row2, vec3 row3 )

create a matrix from 3 rows

mat3( real v[9] )

create a matrix from 9 real values

A 4x4 column-major matrix

• methods
  • identity - set matrix to identity
  • multiply - multiply this matrix with another one
  • multiply_left - left-multiply this matrix with another one
  • multiply2 - multiply two matrices into this one
  • transpose - transpose matrix
  • transpose_from - transpose another matrix into this one
  • invert - invert matrix
  • invert_from - invert another matrix into this one
  • translate - set or multiply a translation matrix
  • translate_v3 - set or multiply a translation matrix (vec3 argument)
  • rotateX - set or multiply a X-axis rotation matrix
  • rotateY - set or multiply a Y-axis rotation matrix
  • rotateZ - set or multiply a Z-axis rotation matrix
  • rotate_axis_angle - set or multiply a custom axis rotation matrix
  • rotate_axis_angle_v3 - set or multiply a custom axis rotation matrix (vec3 argument)
  • scale - set or multiply a scale matrix
  • scale_v3 - set or multiply a scale matrix (vec3 argument)
  • transform - transform a 4D vector
  • transform_pos - transform a 3D position vector
  • transform_normal - transform a 3D normal vector
• read-only properties
  • [int] size - returns 16 - the number of components in this vector
  • [quat] quat - returns the quaternion version of the 3x3 part of this matrix
  • [mat3] mat3 - returns the 3x3 part of this matrix
• read/write properties
  • [real] m[0-3][0-3]
• overloaded operators
  • comparison between subvalues: column-major subvalue order
• other features:
  • cloning support
  • serialization support
  • GC-safe
  • indexing support for indices 0 - 15: returns/sets the specified subvalue
  • tostring = "mat4"
  • dump:

mat4
(
	<m00> <m10> <m20> <m30>
	<m01> <m11> <m21> <m31>
	<m02> <m12> <m22> <m32>
	<m03> <m13> <m23> <m33>
)

mat4.identity()

set the matrix to identity

mat4.multiply( mat4 m )

multiply this matrix and another matrix, putting the other matrix on the right side of multiplication

mat4.multiply_left( mat4 m )

multiply this matrix and another matrix, putting the other matrix on the left side of multiplication

mat4.multiply2( mat4 m1, mat4 m2 )

multiply two matrices into this matrix

mat4.transpose()

transpose this matrix into itself

mat4.transpose_from( mat4 m )

transpose another matrix into this matrix

mat4.invert()

invert this matrix into itself, return if successful

mat4.invert_from( mat4 m )

invert another matrix into this matrix

mat4.translate( real x, real y, real z[, bool reset ])

generate a translation matrix and multiply or set it to this matrix

• if reset is true, the generated matrix is directly set to this matrix
  • otherwise, generated matrix is right-multiplied to this matrix
  • if current matrix is an identity matrix, reset has no effect

mat4.translate_v3( vec3 v[, bool reset ])

generate a translation matrix and multiply or set it to this matrix

• if reset is true, the generated matrix is directly set to this matrix
  • otherwise, generated matrix is right-multiplied to this matrix
  • if current matrix is an identity matrix, reset has no effect

mat4.rotateX( real a[, bool reset ])

generate a rotation matrix (rotation around X axis) and multiply or set it to this matrix

• if reset is true, the generated matrix is directly set to this matrix
  • otherwise, generated matrix is right-multiplied to this matrix
  • if current matrix is an identity matrix, reset has no effect

mat4.rotateY( real a[, bool reset ])

generate a rotation matrix (rotation around Y axis) and multiply or set it to this matrix

• if reset is true, the generated matrix is directly set to this matrix
  • otherwise, generated matrix is right-multiplied to this matrix
  • if current matrix is an identity matrix, reset has no effect

mat4.rotateZ( real a[, bool reset ])

generate a rotation matrix (rotation around Z axis) and multiply or set it to this matrix

• if reset is true, the generated matrix is directly set to this matrix
  • otherwise, generated matrix is right-multiplied to this matrix
  • if current matrix is an identity matrix, reset has no effect

mat4.rotate_axis_angle( real x, real y, real z, real a[, bool reset ])

generate a rotation matrix (rotation around specified axis) and multiply or set it to this matrix

• if reset is true, the generated matrix is directly set to this matrix
  • otherwise, generated matrix is right-multiplied to this matrix
  • if current matrix is an identity matrix, reset has no effect

mat4.rotate_axis_angle( vec3 v, real a[, bool reset ])

generate a rotation matrix (rotation around specified axis) and multiply or set it to this matrix

• if reset is true, the generated matrix is directly set to this matrix
  • otherwise, generated matrix is right-multiplied to this matrix
  • if current matrix is an identity matrix, reset has no effect

mat4.scale( real x, real y, real z[, bool reset ])

generate a scale matrix and multiply or set it to this matrix

• if reset is true, the generated matrix is directly set to this matrix
  • otherwise, generated matrix is right-multiplied to this matrix
  • if current matrix is an identity matrix, reset has no effect

mat4.scale_v3( vec3 v[, bool reset ])

generate a scale matrix and multiply or set it to this matrix

• if reset is true, the generated matrix is directly set to this matrix
  • otherwise, generated matrix is right-multiplied to this matrix
  • if current matrix is an identity matrix, reset has no effect

mat4.transform( vec4 v )

multiply a 4D vector by this matrix

mat4.transform_pos( vec3 v )

multiply a 3D position vector by this matrix

• multiply vec4( v.x, v.y, v.z, 1 ) by this matrix, return vec3( x / w, y / w, z / w )

mat4.transform_normal( vec3 v )

multiply a 3D normal vector by this matrix

• multiply vec4( v.x, v.y, v.z, 0 ) by this matrix, return vec3( x, y, z )

mat4( mat4 m )

copy the matrix

mat4( vec4 row1, vec4 row2, vec4 row3[, vec4 row4 ])

create a matrix from 3 or 4 rows

mat4( real v[16] )

create a matrix from 16 real values

• methods
  • clear - set all values to 0
  • set1 - set all values to 1
  • negate - negate all values
  • assign - copy values from another source
  • negate_from - copy negated values
  • *[_assign] - combine values with arithmetic operations
  • randbox - set values to random between two sources
  • randext - set values to random around source 1 in the range of source 2
  • multiply_add_assign - multiply two sources and add the result to this one
  • lerp_to - linearly interpolate this source and another to the factor of the third one
  • to_*_buffer - convert values to byte buffer, optionally scaling them
• read-only properties
  • [aabb2] aabb2 - returns 2D bounding box of data, assuming data contains 2D vectors
  • [aabb3] aabb3 - returns 3D bounding box of data, assuming data contains 3D vectors
  • [int] size - returns array size - the number of values in this array
  • [int] size2 - returns array size / 2 - the number of vec2 values in this array
  • [int] size3 - returns array size / 3 - the number of vec3 values in this array
  • [int] size4 - returns array size / 4 - the number of vec4 values in this array
  • [int] size16 - returns array size / 16 - the number of mat4 values in this array
• other features:
  • cloning support
  • serialization support
  • GC-safe
  • indexing support for indices 0 - (size-1): returns/sets the specified subvalue
  • tostring = "floatarray"
  • dump: first 64 values, array formatting

• 'source' type can take int, real, vec2, vec3, vec4, mat4 and floatarray sources.
• source values are accessed, indexed by (i % source.size)
• function works on all values inside array

floatarray.clear()

set all values to 0

ifor more info, refer to this page: floatarray data transformation methods

floatarray.set1()

set all values to 1

ifor more info, refer to this page: floatarray data transformation methods

floatarray.negate()

swap the sign on all values

ifor more info, refer to this page: floatarray data transformation methods

floatarray.assign( s1 )

copy values from another source

ifor more info, refer to this page: floatarray data transformation methods

floatarray.negate_from( s1 )

copy negated values from another source

ifor more info, refer to this page: floatarray data transformation methods

floatarray.add( s1, s2 )

add values from two sources to this floatarray (this = s1 + s2)

floatarray.sub( s1, s2 )

subtract values from two sources to this floatarray (this = s1 - s2)

floatarray.mul( s1, s2 )

multiply values from two sources to this floatarray (this = s1 * s2)

floatarray.div( s1, s2 )

divide values from two sources to this floatarray (this = s1 / s2)

floatarray.mod( s1, s2 )

set modulo from two sources to this floatarray (this = s1 % s2)

floatarray.pow( s1, s2 )

set power of two sources to this floatarray (this = s1 ^ s2)

floatarray.add_assign( s1 )

add values from another source to floatarray (this = this + s1)

floatarray.sub_assign( s1 )

subtract values from another source to floatarray (this = this - s1)

floatarray.mul_assign( s1 )

subtract values from another source to floatarray (this = this * s1)

floatarray.div_assign( s1 )

subtract values from another source to floatarray (this = this / s1)

floatarray.mod_assign( s1 )

subtract values from another source to floatarray (this = this % s1)

floatarray.pow_assign( s1 )

subtract values from another source to floatarray (this = this ^ s1)

ifor more info, refer to this page: floatarray data transformation methods

floatarray.randbox( s1, s2 )

set values to random between two sources (this = lerp( s1, s2, randf() ))

ifor more info, refer to this page: floatarray data transformation methods

floatarray.randext( s1, s2 )

set values to random around source 1 in the range of source 2 (this = lerp( s1 - s2, s1 + s2, randf() ))

ifor more info, refer to this page: floatarray data transformation methods

floatarray.multiply_add_assign( s1, s2 )

multiply two sources and add the result to this one (this += s1 * s2)

ifor more info, refer to this page: floatarray data transformation methods

floatarray.lerp_to( s1, s2 )

linearly interpolate this source and another to the factor of the third one (this = lerp( this, s1, s2 ))

ifor more info, refer to this page: floatarray data transformation methods

floatarray.to_int8_buffer( real scale = 1 )

floatarray.to_int16_buffer( real scale = 1 )

floatarray.to_int32_buffer( real scale = 1 )

floatarray.to_int64_buffer( real scale = 1 )

floatarray.to_uint8_buffer( real scale = 1 )

floatarray.to_uint16_buffer( real scale = 1 )

floatarray.to_uint32_buffer( real scale = 1 )

floatarray.to_uint64_buffer( real scale = 1 )

floatarray.to_float32_buffer( real scale = 1 )

floatarray.to_float64_buffer( real scale = 1 )

create a byte buffer from floatarray contents, optionally scaling the values

floatarray_buffer( int size )

create a floatarray of the specified size, filled with zeroes

floatarray([ int/real v0, ... ])

create a floatarray from a list of int/real values

floatarray( array varr )

create a floatarray from an array of int/real values

vec2array([ int/real v0, ... ])

create a floatarray from a list of int/real values (must be a multiple of 2)

vec2array([ vec2 v0, ... ])

create a floatarray from a list of vec2 values

vec2array( array varr )

create a floatarray from an array of vec2 values

vec3array([ int/real v0, ... ])

create a floatarray from a list of int/real values (must be a multiple of 3)

vec3array([ vec3 v0, ... ])

create a floatarray from a list of vec3 values

vec3array( array varr )

create a floatarray from an array of vec3 values

vec4array([ int/real v0, ... ])

create a floatarray from a list of int/real values (must be a multiple of 4)

vec4array([ vec4 v0, ... ])

create a floatarray from a list of vec4 values

vec4array( array varr )

create a floatarray from an array of vec4 values

floatarray_from_int8_buffer( string buffer, scale = 1, stride = 1, offset = 0 )

floatarray_from_int16_buffer( string buffer, scale = 1, stride = 1, offset = 0 )

floatarray_from_int32_buffer( string buffer, scale = 1, stride = 1, offset = 0 )

floatarray_from_int64_buffer( string buffer, scale = 1, stride = 1, offset = 0 )

floatarray_from_uint8_buffer( string buffer, scale = 1, stride = 1, offset = 0 )

floatarray_from_uint16_buffer( string buffer, scale = 1, stride = 1, offset = 0 )

floatarray_from_uint32_buffer( string buffer, scale = 1, stride = 1, offset = 0 )

floatarray_from_uint64_buffer( string buffer, scale = 1, stride = 1, offset = 0 )

floatarray_from_float32_buffer( string buffer, scale = 1, stride = 1, offset = 0 )

floatarray_from_float64_buffer( string buffer, scale = 1, stride = 1, offset = 0 )

create a floatarray from byte buffer, optionally specifying scale, stride and offset to first value

ray_plane_intersect( vec3 ray_pos, vec3 ray_dir, vec4 plane )

tests for an intersection between ray and plane, returning all relevant output data

• if ray is (near-)parallel to plane, false is returned
  • otherwise, signed distance along ray and signed origin distance from plane are returned
  • if signed distance along ray to plane is larger than 0, plane is in front of ray
  • if signed distance from origin to plane is larger than 0, ray origin is in front of the plane

ray_sphere_intersect( vec3 ray_pos, vec3 ray_dir, vec3 sphere_pos, real radius )

tests for an intersection between ray and sphere, returning the distance

• if ray does not intersect sphere, false is returned
  • otherwise, signed distance between ray and sphere is returned
  • if signed distance along ray to sphere is larger than 0, sphere is in front of ray

distance_lines( vec3 a1, vec3 a2, vec3 b1, vec3 b2 )

returns distance between two straight lines, defined by two intersection points

iThis function may not return the expected result if either of the lines has zero length. In such cases, prefer using distance_point_line

distance_line_segments( vec3 a1, vec3 a2, vec3 b1, vec3 b2 )

returns distance between two line segments

iThis function may not return the expected result if either of the lines has zero length. In such cases, prefer using distance_point_line_segment

distance_point_line( vec3 p, vec3 l1, vec3 l2 )

returns distance between point and a straight line, defined by two intersection points

distance_point_line_segment( vec3 p, vec3 l1, vec3 l2 )

returns distance between point and a line segment

• aabb2 [object]
• aabb3 [object]
• color [object]
• floatarray [object]
• mat3 [object]
• mat4 [object]
• quat [object]
• vec2 [object]
• vec3 [object]
• vec4 [object]

• aabb2 [function]
• aabb2.expand( ... ) [function]
• aabb2_intersect [function]
• aabb2v [function]
• aabb3 [function]
• aabb3.expand( ... ) [function]
• aabb3_intersect [function]
• aabb3v [function]
• color [function]
• distance_line_segments [function]
• distance_lines [function]
• distance_point_line [function]
• distance_point_line_segment [function]
• floatarray [function]
• floatarray_buffer [function]
• floatarray_from_*_buffer [function]
• mat3 [function]
• mat4 [function]
• quat [function]
• ray_plane_intersect [function]
• ray_sphere_intersect [function]
• vec2 [function]
• vec2_dot [function]
• vec2array [function]
• vec3 [function]
• vec3_cross [function]
• vec3_dot [function]
• vec3array [function]
• vec4 [function]
• vec4_dot [function]
• vec4array [function]

• XGM_VT - floating point type used throughout the API, alias of float by default
• xgm_vtarray - floatarray data
• xgm_*_iface - object interfaces
• sgs_Create* - xgmath object creation functions
• sgs_Parse* - xgmath object parsing functions
• sgs_ArgCheck_* - xgmath LoadArgs parsing functions

xgm_vtarray

floatarray data

• properties:
  • XGM_VT* data - array of floating point values
  • sgs_SizeVal size - current size of array (current item count)
  • sgs_SizeVal mem - max. size of array (capacity, allocated item count)

sgs_ObjInterface xgm_vec2_iface[1]

interface for vec2 objects

sgs_ObjInterface xgm_vec3_iface[1]

interface for vec3 objects

sgs_ObjInterface xgm_vec4_iface[1]

interface for vec4 objects

sgs_ObjInterface xgm_aabb2_iface[1]

interface for aabb2 objects

sgs_ObjInterface xgm_aabb3_iface[1]

interface for aabb3 objects

sgs_ObjInterface xgm_color_iface[1]

interface for color objects

sgs_ObjInterface xgm_mat4_iface[1]

interface for mat4 objects

sgs_ObjInterface xgm_floatarr_iface[1]

interface for floatarray objects

SGSONE sgs_CreateVec2( SGS_CTX, sgs_Variable* var, XGM_VT x, XGM_VT y )

SGSONE sgs_CreateVec3( SGS_CTX, sgs_Variable* var, XGM_VT x, XGM_VT y, XGM_VT z )

SGSONE sgs_CreateVec4( SGS_CTX, sgs_Variable* var, XGM_VT x, XGM_VT y, XGM_VT z, XGM_VT w )

SGSONE sgs_CreateAABB2( SGS_CTX, sgs_Variable* var, XGM_VT x1, XGM_VT y1, XGM_VT x2, XGM_VT y2 )

SGSONE sgs_CreateAABB3( SGS_CTX, sgs_Variable* var, const XGM_VT* v3f1, const XGM_VT* v3f2 )

SGSONE sgs_CreateColor( SGS_CTX, sgs_Variable* var, XGM_VT r, XGM_VT g, XGM_VT b, XGM_VT a )

SGSONE sgs_CreateQuat( SGS_CTX, sgs_Variable* var, XGM_VT x, XGM_VT y, XGM_VT z, XGM_VT w )

SGSONE sgs_CreateMat3( SGS_CTX, sgs_Variable* var, const XGM_VT* v9f, int transpose )

SGSONE sgs_CreateMat4( SGS_CTX, sgs_Variable* var, const XGM_VT* v16f, int transpose )

SGSONE sgs_CreateFloatArray( SGS_CTX, sgs_Variable* var, const XGM_VT* vfn, sgs_SizeVal size )

SGSONE sgs_CreateVec2p( SGS_CTX, sgs_Variable* var, const XGM_VT* v2f )

SGSONE sgs_CreateVec3p( SGS_CTX, sgs_Variable* var, const XGM_VT* v3f )

SGSONE sgs_CreateVec4p( SGS_CTX, sgs_Variable* var, const XGM_VT* v4f )

SGSONE sgs_CreateAABB2p( SGS_CTX, sgs_Variable* var, const XGM_VT* v4f )

SGSONE sgs_CreateAABB3p( SGS_CTX, sgs_Variable* var, const XGM_VT* v6f )

SGSONE sgs_CreateColorp( SGS_CTX, sgs_Variable* var, const XGM_VT* v4f )

SGSONE sgs_CreateColorvp( SGS_CTX, sgs_Variable* var, const XGM_VT* vf, int numfloats )

SGSONE sgs_CreateQuatp( SGS_CTX, sgs_Variable* var, const XGM_VT* v4f )

push/initialize a variable of the right type to the specified arguments

Notes:

• if var == NULL, variable is pushed to stack
• functions here always return 1 (SGSONE), making them suitable for a "return sgs_Create***" construct
• v*f - array of the specified number of XGM_VT values
• sgs_InitColorvp accepts 0, 1, 2, 3 or 4 for numfloats
  • if 0: R, G, B, A = 0
  • if 1: R, G, B, A = arg1
  • if 2: R, G, B = arg1; A = arg2
  • if 3: R = arg1; G = arg2; B = arg3; A = 1
  • otherwise arguments are mapped to components sequentially
• the p postfix for functions means that function accepts arrays instead of plain values, if that's what the non -p function takes

SGSBOOL sgs_ParseVT( SGS_CTX, sgs_StkIdx item, XGM_VT* out )

SGSBOOL sgs_ParseVec2( SGS_CTX, sgs_StkIdx item, XGM_VT* v2f, int strict )

SGSBOOL sgs_ParseVec3( SGS_CTX, sgs_StkIdx item, XGM_VT* v3f, int strict )

SGSBOOL sgs_ParseVec4( SGS_CTX, sgs_StkIdx item, XGM_VT* v4f, int strict )

SGSBOOL sgs_ParseAABB2( SGS_CTX, sgs_StkIdx item, XGM_VT* v4f )

SGSBOOL sgs_ParseAABB3( SGS_CTX, sgs_StkIdx item, XGM_VT* v6f )

SGSBOOL sgs_ParseColor( SGS_CTX, sgs_StkIdx item, XGM_VT* v4f, int strict )

SGSBOOL sgs_ParseQuat( SGS_CTX, sgs_StkIdx item, XGM_VT* v4f, int strict )

SGSBOOL sgs_ParseMat3( SGS_CTX, sgs_StkIdx item, XGM_VT* v9f )

SGSBOOL sgs_ParseMat4( SGS_CTX, sgs_StkIdx item, XGM_VT* v16f )

SGSBOOL sgs_ParseFloatArray( SGS_CTX, sgs_StkIdx item, XGM_VT** vfa, sgs_SizeVal* osz )

parse the specified stack item to retrieve object data

• strict means that only the object of the specified type is allowed to be parsed
  • otherwise, real values are parsed too

int sgs_ArgCheck_Vec2( SGS_CTX, int argid, va_list* args, int flags )

int sgs_ArgCheck_Vec3( SGS_CTX, int argid, va_list* args, int flags )

int sgs_ArgCheck_Vec4( SGS_CTX, int argid, va_list* args, int flags )

int sgs_ArgCheck_AABB2( SGS_CTX, int argid, va_list* args, int flags )

int sgs_ArgCheck_AABB3( SGS_CTX, int argid, va_list* args, int flags )

int sgs_ArgCheck_Color( SGS_CTX, int argid, va_list* args, int flags )

int sgs_ArgCheck_Quat( SGS_CTX, int argid, va_list* args, int flags )

int sgs_ArgCheck_Mat3( SGS_CTX, int argid, va_list* args, int flags )

int sgs_ArgCheck_Mat4( SGS_CTX, int argid, va_list* args, int flags )

int sgs_ArgCheck_FloatArray( SGS_CTX, int argid, va_list* args, int flags )

argument parsing functions for sgs_LoadArgs* function family

• variable argument list expectations if output is enabled:
  • Vec2: XGM_VT[2]
  • Vec3: XGM_VT[3]
  • Vec4: XGM_VT[4]
  • AABB2: XGM_VT[4]
  • AABB3: XGM_VT[6]
  • Color: XGM_VT[4]
  • Quat: XGM_VT[4]
  • Mat3: XGM_VT[9]
  • Mat4: XGM_VT[16]
  • FloatArray: xgm_vtarray**

• xgm_*_iface [interfaces]
• xgm_vtarray [struct]

• sgs_ArgCheck_* [functions]
• sgs_Create* [functions]
• sgs_Parse* [functions]