graphmath v0.5.2 → Overview → Graphmath → Vec3

Graphmath.Vec3

Summary
Types
Functions

This is the 3D mathematics library for graphmath.

This submodule handles 3D vectors using tuples of floats.

Summary
↑

add(a, b)	`add( a, b)` adds two `vec3`s
create()	`create()` creates a zeroed `vec3`
create(vec)	`create(vec)` creates a `vec3` from a list of 3 or more floats
create(x, y, z)	`create(x,y,z)` creates a `vec3` of value (x,y,z)
cross(a, b)	`cross( a, b)` finds the cross productof one `vec3` with another `vec3`
dot(a, b)	`dot( a, b)` finds the dot (inner) product of one `vec3` with another `vec3`
length(a)	`length(a)` finds the length (Eucldiean or L2 norm) of a `vec3`
length_manhattan(a)	`length_manhattan(a)` finds the Manhattan (L1 norm) length of a `vec3`
length_squared(a)	`length_squared(a)` finds the square of the length of a `vec3`
lerp(a, b, t)	`lerp(a,b,t)` linearly interpolates between one `vec3` and another `vec3` along an interpolant
multiply(a, b)	`multiply( a, b)` multiplies element-wise a `vec3` by another `vec3`
near(a, b, distance)	`near(a,b, distance)` checks whether two `vec3`s are within a certain distance of each other
normalize(a)	`normalize(a)` finds the unit vector with the same direction as a `vec3`
rotate(v, k, theta)	`rotate( v, k, theta)` rotates a vector (v) about a unit vector (k) by theta radians
scale(a, scale)	`scale( a, scale)` uniformly scales a `vec3`
subtract(a, b)	`subtract(a, b)` subtracts one `vec3` from another `vec3`

Types ↑

vec3 :: {float, float, float}

Functions

add(a, b)

(function) # ↑

Specs:

add(vec3, vec3) :: vec3

add( a, b) adds two vec3s.

a is the first vec3.

b is the second vec3.

It returns a vec3 of the form { a_x + b_x, a_y + b_y, a_z + b_z }.

create()

(function) # ↑

Specs:

create :: vec3

create() creates a zeroed vec3.

It takes no arguments.

It returns a vec3 of the form { 0.0, 0.0, 0.0 }.

create(vec)

(function) # ↑

Specs:

create([float]) :: vec3

create(vec) creates a vec3 from a list of 3 or more floats.

vec is a list of 3 or more floats.

It returns a vec3 of the form {x,y,z}, where x, y, and z are the first three elements in vec.

create(x, y, z)

(function) # ↑

Specs:

create(float, float, float) :: vec3

create(x,y,z) creates a vec3 of value (x,y,z).

x is the first element of the vec3 to be created.

y is the second element of the vec3 to be created.

z is the third element of the vec3 to be created.

It returns a vec3 of the form {x,y,z}.

cross(a, b)

(function) # ↑

Specs:

cross(vec3, vec3) :: vec3

cross( a, b) finds the cross productof one vec3 with another vec3.

a is the first vec3.

b is the second vec3.

It returns a float of the value ( a_yb_z - a_zb_y, a_zb_x - a_xb_z, a_xb_y - a_yb_x).

The cross product of two vectors is a vector perpendicular to the two source vectors. Its magnitude will be the area of the parallelogram made by the two souce vectors.

dot(a, b)

(function) # ↑

Specs:

dot(vec3, vec3) :: float

dot( a, b) finds the dot (inner) product of one vec3 with another vec3.

a is the first vec3.

b is the second vec3.

It returns a float of the value (a_xb_x + a_yb_y + a_zb_z).

length(a)

(function) # ↑

Specs:

length(vec3) :: float

length(a) finds the length (Eucldiean or L2 norm) of a vec3.

a is the vec3 to find the length of.

It returns a float of the value (sqrt( a_x² + a_y² + a_z²)).

length_manhattan(a)

(function) # ↑

Specs:

length_manhattan(vec3) :: float

length_manhattan(a) finds the Manhattan (L1 norm) length of a vec3.

a is the vec3 to find the Manhattan length of.

It returns a float of the value (a_x + a_y + a_z).

The Manhattan length is the sum of the components.

length_squared(a)

(function) # ↑

Specs:

length_squared(vec3) :: float

length_squared(a) finds the square of the length of a vec3.

a is the vec3 to find the length squared of.

It returns a float of the value a_x² + a_y² + a_z².

In many cases, this is sufficient for comparisons and avoids a square root.

lerp(a, b, t)

(function) # ↑

Specs:

lerp(vec3, vec3, float) :: vec3

lerp(a,b,t) linearly interpolates between one vec3 and another vec3 along an interpolant.

a is the starting vec3.

b is the ending vec3.

t is the interpolant float, on the domain [0,1].

It returns a vec3 of the form (1-t)a - (t)b.

The interpolant t is on the domain [0,1]. Behavior outside of that is undefined.

multiply(a, b)

(function) # ↑

Specs:

multiply(vec3, vec3) :: vec3

multiply( a, b) multiplies element-wise a vec3 by another vec3.

a is the vec3 multiplicand.

b is the vec3 multiplier.

It returns a vec3 of the form { a_xb_x, a_yb_y, a_zb_z }.

near(a, b, distance)

(function) # ↑

Specs:

near(vec3, vec3, float) :: boolean

near(a,b, distance) checks whether two vec3s are within a certain distance of each other.

a is the first vec3.

b is the second vec3.

distance is the distance between them as a float.

normalize(a)

(function) # ↑

Specs:

normalize(vec3) :: vec3

normalize(a) finds the unit vector with the same direction as a vec3.

a is the vec3 to be normalized.

It returns a vec3 of the form {normx, normy, normz}.

This is done by dividing each component by the vector’s magnitude.

rotate(v, k, theta)

(function) # ↑

Specs:

rotate(vec3, vec3, float) :: vec3

rotate( v, k, theta) rotates a vector (v) about a unit vector (k) by theta radians.

v is the vec3 to be rotated.

k is the vec3 axis of rotation. It must be of unit length.

theta is the angle in radians to rotate as a float.

This uses the Formula of Rodriguez:

V_rot = Vcos(theta) + (K x V)sin(theta) + K(K dot V)(1-cos(theta))

scale(a, scale)

(function) # ↑

Specs:

scale(vec3, float) :: vec3

scale( a, scale) uniformly scales a vec3.

a is the vec3 to be scaled.

scale is the float to scale each element of a by.

It returns a tuple of the form { a_xscale, a_yscale, a_zscale }.

subtract(a, b)

(function) # ↑

Specs:

subtract(vec3, vec3) :: vec3

subtract(a, b) subtracts one vec3 from another vec3.

a is the vec3 minuend.

b is the vec3 subtrahend.

It returns a vec3 of the form { a_x - b_x, a_y - b_y, a_z - b_z }.

(the terminology was found here).

Graphmath.Vec3

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Functions

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