Math Common Functions

See Also

variable abs (variable arg)

Arguments

• variable arg - Argument. Can be the following types:
  • int
  • long
  • float
  • double
  • vec3
  • vec4
  • dvec3
  • dvec4

Return value

Variable bezier (vec4 times, variable values, float time)

Arguments

• vec4 times - Control points on the T axis (i.e. horizontal X axis).
• variable values - Control points on the V axis (i.e. vertical Y axis). They can either be of vec4 or dvec4 types.
• float time - Time t.

Return value

variable ceil (variable arg)

Arguments

• variable arg - Argument. Can be the following types:
  • int
  • long
  • float
  • double
  • vec3
  • vec4
  • dvec3
  • dvec4

Return value

• float for int, long, float arguments
• double for double arguments
• vec4 for vec4 arguments
• dvec3 for dvec3 arguments
• dvec4 for dvec4 arguments

Examples

float a = ceil(2.3) // a = 3.0

variable clamp (variable v, variable min, variable max)

Arguments

• variable v - Argument. Can be the following types:
  • int
  • long
  • float
  • double
  • vec3
  • vec4
  • dvec3
  • dvec4
  • ivec3
  • ivec4
• variable min - Minimum limit. Type must be the same as the type of v.

  If the first argument is int, it can also be string:

  • If a string is empty, it will equal to int(0).
  • If a string is nonempty, it will equal to int(1).
• variable max - Maximum limit. Type must be the same as the type of v.

  If the first argument is int, it can also be string:

  • If a string is empty, it will equal to int(0).
  • If a string is nonempty, it will equal to int(1).

Return value

int compare (variable v0, variable v1, variable epsilon = 1e-6)

Compares two variables of the same type according to the specified degree of precision. The following formula is used:

fabs(v0 - v1) < (fabs(v0) + fabs(v1) + 1.0) * eps

Arguments

• variable v0 - Variable of one of the following types:
  • float
  • double
  • vec3
  • vec4
  • dvec3
  • dvec4
  • mat4
  • dmat4
  • quat
• variable v1 - Variable of the same type as v0.
• variable epsilon - Epsilon. Can be the following types:
  • int
  • long
  • float
  • double

Return value

Variable cross (variable v0, variable v1)

Arguments

• variable v0 - First vector. Can be of the following types:
  • vec3
  • dvec3
  • ivec3
• variable v1 - Second vector (of the same type as v0 vector).

Return value

Variable dot3 (variable v0, variable v1)

Arguments

• variable v0 - First vector. Can be of the following types:
  • vec3
  • vec4
  • dvec3
  • dvec4
• variable v1 - Second vector. Can be one of similar types as v0.

Return value

• float if case of vec3 or vec4
• double if case of dvec3 or dvec4

Examples

printf("%f\n",dot3(vec3(1,2,3),vec3(1,2,3)));
printf("%f\n",dot3(vec3(1,2,3),vec4(1,2,3,4)));
/*
result is:
14.000000
14.000000
*/

Variable dot (variable v0, variable v1)

• It is possible to obtain a dot product of vec3 and vec4, as well as a dot product of dvec3 and dvec4. In this case, w component of the four-component vector is added to the dot product of first three components of vectors.
• A dot product of ivec3, ivec4 and quat requires the second argument to be exactly of the same type.

Arguments

• variable v0 - First argument. Can be of the following types:
  • vec3
  • vec4
  • dvec3
  • dvec4
  • ivec3
  • ivec4
  • quat
• variable v1 - Second argumet. Can be one of the same of similar types as v0.

Return value

• float if case of vec3 or vec4
• double if case of dvec3 or dvec4
• int if case of ivec3 or ivec4

Examples

printf("%f\n",dot(vec3(1,2,3),vec3(1,2,3)));
printf("%f\n",dot(vec3(1,2,3),vec4(1,2,3,4)));
/*
result is:
14.000000
18.000000
*/

variable floor (variable arg)

Arguments

• variable arg - Argument. Can be the following types:
  • int
  • long
  • float
  • double
  • vec3
  • vec4
  • dvec3
  • dvec4

Return value

• float for int, long, float arguments
• double for double arguments
• vec4 for vec4 arguments
• dvec3 for dvec3 arguments
• dvec4 for dvec4 arguments

Examples

float a = floor(2.3) // a = 2.0

variable frac (variable arg)

Arguments

• variable arg - Argument. Can be the following types:
  • int
  • long
  • float
  • double
  • vec3
  • vec4
  • dvec3
  • dvec4

Return value

Fraction part of arg (arg - floor(arg)). The type of returned value will depend on the argument type:

• float for int, long, float arguments
• double for double arguments
• vec4 for vec4 arguments
• dvec3 for dvec3 arguments
• dvec4 for dvec4 arguments

Variable length2 (variable vector)

Arguments

• variable vector - A vector. Can be the following types:
  • vec3
  • vec4
  • dvec3
  • dvec4
  • ivec3
  • ivec4

Return value

• float for vec3 and vec4 arguments
• double for dvec3 and dvec4 arguments
• int for ivec3 and ivec4 arguments

Variable length (variable vector)

Arguments

• variable vector - A vector. Can be the following types:
  • vec3
  • vec4
  • dvec3
  • dvec4

Return value

• float for vec3 and vec4 arguments
• double for dvec3 and dvec4 arguments

Variable lerp (variable v0, variable v1, variable k)

Arguments

• variable v0 - Start value. Can be the following types:
  • int
  • long
  • float
  • double
  • vec3
  • vec4
  • dvec3
  • dvec4
  • ivec3
  • ivec4
  • mat4
  • dmat4
  • quat
• variable v1 - End value. Must be the same type as v0.
• variable k - Value from 0 to 1 indicating the weight of v1. Can be the following types:
  • int
  • long
  • float
  • double
  • string if arguments are ivec3 or ivec4:
    • If a string is empty, it will equal to int(0).
    • If a string is nonempty, it will equal to int(1).

Return value

variable max (variable arg1, variable arg2)

Arguments

• variable arg1 - First argument. Can be the following types:
  • int
  • long
  • float
  • double
  • vec3
  • vec4
  • dvec3
  • dvec4
  • ivec3
  • ivec4
• variable arg2 - Second argument. Type must be the same as the type of arg1.

  If arg1 is int, the second argument can also be string:

  • If a string is empty, it will equal to int(0).
  • If a string is nonempty, it will equal to int(1).

Return value

variable min (variable arg1, variable arg2)

Arguments

• variable arg1 - First argument. Can be the following types:
  • int
  • long
  • float
  • double
  • vec3
  • vec4
  • dvec3
  • dvec4
  • ivec3
  • ivec4
• variable arg2 - Second argument. Type must be the same as the type of arg1.

  If arg1 is int, the second argument can be string:

  • If a string is empty, it will equal to int(0).
  • If a string is nonempty, it will equal to int(1).

Return value

Variable normalize3 (variable v)

• Normalizes the X, Y, Z components of the given vector.
• Recalculates the w component of the given quaternion.

Arguments

• variable v - Argument of one of the following types:
  • vec4 v - A vector of 4 float components.
  • dvec4 v - A vector of 4 double components.
  • quat v - A quaternion.

Return value

Examples

You can use the normalize3() function when you need to restore the w component of the quaternion, for example:

vec3 t = vec3(1.0f,0.0f,0.0f); // the tangent basis: tangent vector
vec3 b = vec3(0.0f,1.0f,0.0f); // binormal vector
vec3 n = vec3(0.0f,0.0f,1.0f); // normal vector
vec4 tangent = orthoTangent(t,b,n); // this is the mesh compressed tangent vector

quat compact_tangent_quat = quat(tangent); // convert vec4 to quat; currently the last component of the tangent vector contains the sign of the binormal
quat normalized_quat = normalize3(compact_tangent_quat); // normalize quat; now you have the correct quaternion

variable normalize (variable vector)

Arguments

• variable vector - A vector. Can be the following types:
  • vec3
  • vec4
  • dvec3
  • dvec4
  • quat

Return value

int npot (int arg)

Arguments

• int arg - Argument.

Return value

variable rcp (variable arg)

Arguments

• variable arg - Argument. Can be the following types:
  • int
  • long
  • float
  • double
  • vec3
  • vec4
  • dvec3
  • dvec4

Return value

• float for int, long, float arguments
• double for double arguments
• vec4 for vec4 arguments
• dvec3 for dvec3 arguments
• dvec4 for dvec4 arguments

Variable reflect (variable v0, variable v1)

Arguments

• variable v0 - Vector to reflect (vec3 or dvec3)
• variable v1 - Vector, from which v0 will be reflected (of the same type as v0 vector).

Return value

variable saturate (variable v)

Arguments

• variable v - Argument. Can be the following types:
  • int
  • long
  • float
  • double
  • vec3
  • vec4
  • dvec3
  • dvec4
  • ivec3
  • ivec4

Return value

variable sign (variable arg)

Arguments

• variable arg - Argument. Can be the following types:
  • int
  • long
  • float
  • double
  • vec3
  • vec4
  • dvec3
  • dvec4

Return value

• float for int, long, float arguments
• double for double arguments
• vec4 for vec4 arguments
• dvec3 for dvec3 arguments
• dvec4 for dvec4 arguments

int udiv (int x, int y)

Arguments

• int x - The first argument.
• int y - The second argument.

Return value