## Vectors

Vectors — Functions for handling single precision float vectors.

## Synopsis

    #define             cogl_vector3_init
    #define             cogl_vector3_init_zero
    #define             cogl_vector3_equal
    #define             cogl_vector3_equal_with_epsilon
    #define             cogl_vector3_copy
    #define             cogl_vector3_free
    #define             cogl_vector3_invert
    #define             cogl_vector3_add
    #define             cogl_vector3_subtract
    #define             cogl_vector3_multiply_scalar
    #define             cogl_vector3_divide_scalar
    #define             cogl_vector3_normalize
    #define             cogl_vector3_magnitude
    #define             cogl_vector3_cross_product
    #define             cogl_vector3_dot_product
    #define             cogl_vector3_distance

## Description

This exposes a utility API that can be used for basic manipulation of 3 component float vectors.

## Details

### cogl_vector3_init

    #define cogl_vector3_init cogl_vector3_init_EXP

Initializes a 3 component, single precision float vector which can then be manipulated with the cogl_vector convenience APIs. Vectors can also be used in places where a "point" is often desired.

`vector` : | The CoglVector3 you want to initialize
`x` : | The x component
`y` : | The y component
`z` : | The z component

Since 1.4

Stability Level: Unstable

### cogl_vector3_init_zero

    #define cogl_vector3_init_zero cogl_vector3_init_zero_EXP

Initializes a 3 component, single precision float vector with zero for each component.

`vector` : | The CoglVector3 you want to initialize

Since 1.4

Stability Level: Unstable

### cogl_vector3_equal

    #define cogl_vector3_equal cogl_vector3_equal_EXP

Compares the components of two vectors and returns TRUE if they are the same.

The comparison of the components is done with the '==' operator such that -0 is considered equal to 0, but otherwise there is no fuzziness such as an epsilon to consider vectors that are essentially identical except for some minor precision error differences due to the way they have been manipulated.

`v1` : | The first CoglVector3 you want to compare
`v2` : | The second CoglVector3 you want to compare
Returns : | TRUE if the vectors are equal else FALSE.

Since 1.4

Stability Level: Unstable

### cogl_vector3_equal_with_epsilon

    #define cogl_vector3_equal_with_epsilon cogl_vector3_equal_with_epsilon_EXP

Compares the components of two vectors using the given epsilon and returns TRUE if they are the same, using an internal epsilon for comparing the floats.

Each component is compared against the epsilon value in this way:

    1

    if (fabsf (vector0->x - vector1->x) < epsilon)

`vector0` : | The first CoglVector3 you want to compare
`vector1` : | The second CoglVector3 you want to compare
`epsilon` : | The allowable difference between components to still be considered equal
Returns : | TRUE if the vectors are equal else FALSE.

Since 1.4

Stability Level: Unstable

### cogl_vector3_copy

    #define cogl_vector3_copy cogl_vector3_copy_EXP

Allocates a new CoglVector3 structure on the heap initializing the components from the given `vector` and returns a pointer to the newly allocated vector. You should free the memory using `cogl_vector3_free()`

`vector` : | The CoglVector3 you want to copy
Returns : | A newly allocated CoglVector3.

Since 1.4

Stability Level: Unstable

### cogl_vector3_free

    #define cogl_vector3_free cogl_vector3_free_EXP

Frees a CoglVector3 that was previously allocated with `cogl_vector_copy()`

`vector` : | The CoglVector3 you want to free

Since 1.4

Stability Level: Unstable

### cogl_vector3_invert

    #define cogl_vector3_invert cogl_vector3_invert_EXP

Inverts/negates all the components of the given `vector`.

`vector` : | The CoglVector3 you want to manipulate

Since 1.4

Stability Level: Unstable

### cogl_vector3_add

    #define cogl_vector3_add cogl_vector3_add_EXP

Adds each of the corresponding components in vectors `a` and `b` storing the results in `result`.

`result` : | Where you want the result written
`a` : | The first vector operand
`b` : | The second vector operand

Since 1.4

Stability Level: Unstable

### cogl_vector3_subtract

    #define cogl_vector3_subtract cogl_vector3_subtract_EXP

Subtracts each of the corresponding components in vector `b` from `a` storing the results in `result`.

`result` : | Where you want the result written
`a` : | The first vector operand
`b` : | The second vector operand

Since 1.4

Stability Level: Unstable

### cogl_vector3_multiply_scalar

    #define cogl_vector3_multiply_scalar cogl_vector3_multiply_scalar_EXP

Multiplies each of the `vector` components by the given scalar.

`vector` : | The CoglVector3 you want to manipulate
`scalar` : | The scalar you want to multiply the vector components by

Since 1.4

Stability Level: Unstable

### cogl_vector3_divide_scalar

    #define cogl_vector3_divide_scalar cogl_vector3_divide_scalar_EXP

Divides each of the `vector` components by the given scalar.

`vector` : | The CoglVector3 you want to manipulate
`scalar` : | The scalar you want to divide the vector components by

Since 1.4

Stability Level: Unstable

### cogl_vector3_normalize

    #define cogl_vector3_normalize cogl_vector3_normalize_EXP

Updates the vector so it is a "unit vector" such that the `vector`s magnitude or length is equal to 1.

`vector` : | The CoglVector3 you want to manipulate

Since 1.4

Stability Level: Unstable

### cogl_vector3_magnitude

    #define cogl_vector3_magnitude cogl_vector3_magnitude_EXP

Calculates the scalar magnitude or length of `vector`.

`vector` : | The CoglVector3 you want the magnitude for
Returns : | The magnitude of `vector`.

Since 1.4

Stability Level: Unstable

### cogl_vector3_cross_product

    #define cogl_vector3_cross_product cogl_vector3_cross_product_EXP

Calculates the cross product between the two vectors `u` and `v`.

The cross product is a vector perpendicular to both `u` and `v`. This can be useful for calculating the normal of a polygon by creating two vectors in its plane using the polygons vertices and taking their cross product.

If the two vectors are parallel then the cross product is 0.

You can use a right hand rule to determine which direction the perpendicular vector will point: If you place the two vectors tail, to tail and imagine grabbing the perpendicular line that extends through the common tail with your right hand such that you fingers rotate in the direction from `u` to `v` then the resulting vector points along your extended thumb.

`result` : | Where you want the result written
`u` : | Your first CoglVector3
`v` : | Your second CoglVector3
Returns : | The cross product between two vectors `u` and `v`.

Since 1.4

Stability Level: Unstable

### cogl_vector3_dot_product

    #define cogl_vector3_dot_product cogl_vector3_dot_product_EXP

Calculates the dot product of the two CoglVector3s. This can be used to determine the magnitude of one vector projected onto another. (for example a surface normal)

For example if you have a polygon with a given normal vector and some other point for which you want to calculate its distance from the polygon, you can create a vector between one of the polygon vertices and that point and use the dot product to calculate the magnitude for that vector but projected onto the normal of the polygon. This way you don't just get the distance from the point to the edge of the polygon you get the distance from the point to the nearest part of the polygon.

### Note

If you don't use a unit length normal in the above example then you would then also have to divide the result by the magnitude of the normal

The dot product is calculated as:

    1

    (a->x * b->x + a->y * b->y + a->z * b->z)

For reference, the dot product can also be calculated from the angle between two vectors as:

    1

    |a||b|cos𝜃

`a` : | Your first CoglVector3
`b` : | Your second CoglVector3
Returns : | The dot product of two vectors.

Since 1.4

Stability Level: Unstable

### cogl_vector3_distance

    #define cogl_vector3_distance cogl_vector3_distance_EXP

If you consider the two given vectors as (x,y,z) points instead then this will compute the distance between those two points.

`a` : | The first point
`b` : | The second point
Returns : | The distance between two points given as `CoglVector3`s

Since 1.4

Stability Level: Unstable