## GimpVector

GimpVector — Utilities to set up and manipulate vectors.

## Synopsis

    struct      GimpVector2;
    struct      GimpVector3;
    struct      GimpVector4;
    GimpVector2 gimp_vector2_new                (gdouble x,
                                                 gdouble y);
    void        gimp_vector2_set                (GimpVector2 *vector,
                                                 gdouble x,
                                                 gdouble y);
    gdouble     gimp_vector2_length             (const GimpVector2 *vector);
    gdouble     gimp_vector2_length_val         (GimpVector2 vector);
    void        gimp_vector2_mul                (GimpVector2 *vector,
                                                 gdouble factor);
    GimpVector2 gimp_vector2_mul_val            (GimpVector2 vector,
                                                 gdouble factor);
    void        gimp_vector2_normalize          (GimpVector2 *vector);
    GimpVector2 gimp_vector2_normalize_val      (GimpVector2 vector);
    void        gimp_vector2_neg                (GimpVector2 *vector);
    GimpVector2 gimp_vector2_neg_val            (GimpVector2 vector);
    void        gimp_vector2_add                (GimpVector2 *result,
                                                 const GimpVector2 *vector1,
                                                 const GimpVector2 *vector2);
    GimpVector2 gimp_vector2_add_val            (GimpVector2 vector1,
                                                 GimpVector2 vector2);
    void        gimp_vector2_sub                (GimpVector2 *result,
                                                 const GimpVector2 *vector1,
                                                 const GimpVector2 *vector2);
    GimpVector2 gimp_vector2_sub_val            (GimpVector2 vector1,
                                                 GimpVector2 vector2);
    gdouble     gimp_vector2_inner_product      (const GimpVector2 *vector1,
                                                 const GimpVector2 *vector2);
    gdouble     gimp_vector2_inner_product_val  (GimpVector2 vector1,
                                                 GimpVector2 vector2);
    GimpVector2 gimp_vector2_cross_product      (const GimpVector2 *vector1,
                                                 const GimpVector2 *vector2);
    GimpVector2 gimp_vector2_cross_product_val  (GimpVector2 vector1,
                                                 GimpVector2 vector2);
    void        gimp_vector2_rotate             (GimpVector2 *vector,
                                                 gdouble alpha);
    GimpVector2 gimp_vector2_rotate_val         (GimpVector2 vector,
                                                 gdouble alpha);
    GimpVector3 gimp_vector3_new                (gdouble x,
                                                 gdouble y,
                                                 gdouble z);
    void        gimp_vector3_set                (GimpVector3 *vector,
                                                 gdouble x,
                                                 gdouble y,
                                                 gdouble z);
    gdouble     gimp_vector3_length             (const GimpVector3 *vector);
    gdouble     gimp_vector3_length_val         (GimpVector3 vector);
    void        gimp_vector3_mul                (GimpVector3 *vector,
                                                 gdouble factor);
    GimpVector3 gimp_vector3_mul_val            (GimpVector3 vector,
                                                 gdouble factor);
    void        gimp_vector3_normalize          (GimpVector3 *vector);
    GimpVector3 gimp_vector3_normalize_val      (GimpVector3 vector);
    void        gimp_vector3_neg                (GimpVector3 *vector);
    GimpVector3 gimp_vector3_neg_val            (GimpVector3 vector);
    void        gimp_vector3_add                (GimpVector3 *result,
                                                 const GimpVector3 *vector1,
                                                 const GimpVector3 *vector2);
    GimpVector3 gimp_vector3_add_val            (GimpVector3 vector1,
                                                 GimpVector3 vector2);
    void        gimp_vector3_sub                (GimpVector3 *result,
                                                 const GimpVector3 *vector1,
                                                 const GimpVector3 *vector2);
    GimpVector3 gimp_vector3_sub_val            (GimpVector3 vector1,
                                                 GimpVector3 vector2);
    gdouble     gimp_vector3_inner_product      (const GimpVector3 *vector1,
                                                 const GimpVector3 *vector2);
    gdouble     gimp_vector3_inner_product_val  (GimpVector3 vector1,
                                                 GimpVector3 vector2);
    GimpVector3 gimp_vector3_cross_product      (const GimpVector3 *vector1,
                                                 const GimpVector3 *vector2);
    GimpVector3 gimp_vector3_cross_product_val  (GimpVector3 vector1,
                                                 GimpVector3 vector2);
    void        gimp_vector3_rotate             (GimpVector3 *vector,
                                                 gdouble alpha,
                                                 gdouble beta,
                                                 gdouble gamma);
    GimpVector3 gimp_vector3_rotate_val         (GimpVector3 vector,
                                                 gdouble alpha,
                                                 gdouble beta,
                                                 gdouble gamma);
    void        gimp_vector_2d_to_3d            (gint sx,
                                                 gint sy,
                                                 gint w,
                                                 gint h,
                                                 gint x,
                                                 gint y,
                                                 const GimpVector3 *vp,
                                                 GimpVector3 *p);
    GimpVector3 gimp_vector_2d_to_3d_val        (gint sx,
                                                 gint sy,
                                                 gint w,
                                                 gint h,
                                                 gint x,
                                                 gint y,
                                                 GimpVector3 vp,
                                                 GimpVector3 p);
    void        gimp_vector_3d_to_2d            (gint sx,
                                                 gint sy,
                                                 gint w,
                                                 gint h,
                                                 gdouble *x,
                                                 gdouble *y,
                                                 const GimpVector3 *vp,
                                                 const GimpVector3 *p);

## Description

Utilities to set up and manipulate vectors.

## Details

### struct GimpVector2

    struct GimpVector2 {

      gdouble x, y;
    };

A two dimensional vector.

### struct GimpVector3

    struct GimpVector3 {

      gdouble x, y, z;
    };

A three dimensional vector.

### struct GimpVector4

    struct GimpVector4 {

      gdouble x, y, z, w;
    };

A four dimensional vector.

### gimp_vector2_new ()

    GimpVector2 gimp_vector2_new                (gdouble x,
                                                 gdouble y);

Creates a GimpVector2 of coordinates `x` and `y`.

`x` : | the X coordinate.
`y` : | the Y coordinate.
Returns : | the resulting GimpVector2.

### gimp_vector2_set ()

    void        gimp_vector2_set                (GimpVector2 *vector,
                                                 gdouble x,
                                                 gdouble y);

Sets the X and Y coordinates of `vector` to `x` and `y`.

`vector` : | a pointer to a GimpVector2.
`x` : | the X coordinate.
`y` : | the Y coordinate.

### gimp_vector2_length ()

    gdouble     gimp_vector2_length             (const GimpVector2 *vector);

Computes the length of a 2D vector.

`vector` : | a pointer to a GimpVector2.
Returns : | the length of `vector` (a positive gdouble).

### gimp_vector2_length_val ()

    gdouble     gimp_vector2_length_val         (GimpVector2 vector);

This function is identical to `gimp_vector2_length()` but the vector is passed by value rather than by reference.

`vector` : | a GimpVector2.
Returns : | the length of `vector` (a positive gdouble).

### gimp_vector2_mul ()

    void        gimp_vector2_mul                (GimpVector2 *vector,
                                                 gdouble factor);

Multiplies each component of the `vector` by `factor`. Note that this is equivalent to multiplying the vectors length by `factor`.

`vector` : | a pointer to a GimpVector2.
`factor` : | a scalar.

### gimp_vector2_mul_val ()

    GimpVector2 gimp_vector2_mul_val            (GimpVector2 vector,
                                                 gdouble factor);

This function is identical to `gimp_vector2_mul()` but the vector is passed by value rather than by reference.

`vector` : | a GimpVector2.
`factor` : | a scalar.
Returns : | the resulting GimpVector2.

### gimp_vector2_normalize ()

    void        gimp_vector2_normalize          (GimpVector2 *vector);

Normalizes the `vector` so the length of the `vector` is 1.0. The nul vector will not be changed.

`vector` : | a pointer to a GimpVector2.

### gimp_vector2_normalize_val ()

    GimpVector2 gimp_vector2_normalize_val      (GimpVector2 vector);

This function is identical to `gimp_vector2_normalize()` but the vector is passed by value rather than by reference.

`vector` : | a GimpVector2.
Returns : | a GimpVector2 parallel to `vector`, pointing in the same direction but with a length of 1.0.

### gimp_vector2_neg ()

    void        gimp_vector2_neg                (GimpVector2 *vector);

Negates the `vector` (i.e. negate all its coordinates).

`vector` : | a pointer to a GimpVector2.

### gimp_vector2_neg_val ()

    GimpVector2 gimp_vector2_neg_val            (GimpVector2 vector);

This function is identical to `gimp_vector2_neg()` but the vector is passed by value rather than by reference.

`vector` : | a GimpVector2.
Returns : | the negated GimpVector2.

### gimp_vector2_add ()

    void        gimp_vector2_add                (GimpVector2 *result,
                                                 const GimpVector2 *vector1,
                                                 const GimpVector2 *vector2);

Computes the sum of two 2D vectors. The resulting GimpVector2 is stored in `result`.

`result` : | destination for the resulting GimpVector2.
`vector1` : | a pointer to the first GimpVector2.
`vector2` : | a pointer to the second GimpVector2.

### gimp_vector2_add_val ()

    GimpVector2 gimp_vector2_add_val            (GimpVector2 vector1,
                                                 GimpVector2 vector2);

This function is identical to `gimp_vector2_add()` but the vectors are passed by value rather than by reference.

`vector1` : | the first GimpVector2.
`vector2` : | the second GimpVector2.
Returns : | the resulting GimpVector2.

### gimp_vector2_sub ()

    void        gimp_vector2_sub                (GimpVector2 *result,
                                                 const GimpVector2 *vector1,
                                                 const GimpVector2 *vector2);

Computes the difference of two 2D vectors (`vector1` minus `vector2`). The resulting GimpVector2 is stored in `result`.

`result` : | the destination for the resulting GimpVector2.
`vector1` : | a pointer to the first GimpVector2.
`vector2` : | a pointer to the second GimpVector2.

### gimp_vector2_sub_val ()

    GimpVector2 gimp_vector2_sub_val            (GimpVector2 vector1,
                                                 GimpVector2 vector2);

This function is identical to `gimp_vector2_sub()` but the vectors are passed by value rather than by reference.

`vector1` : | the first GimpVector2.
`vector2` : | the second GimpVector2.
Returns : | the resulting GimpVector2.

### gimp_vector2_inner_product ()

    gdouble     gimp_vector2_inner_product      (const GimpVector2 *vector1,
                                                 const GimpVector2 *vector2);

Computes the inner (dot) product of two 2D vectors. This product is zero if and only if the two vectors are orthognal.

`vector1` : | a pointer to the first GimpVector2.
`vector2` : | a pointer to the second GimpVector2.
Returns : | The inner product.

### gimp_vector2_inner_product_val ()

    gdouble     gimp_vector2_inner_product_val  (GimpVector2 vector1,
                                                 GimpVector2 vector2);

This function is identical to `gimp_vector2_inner_product()` but the vectors are passed by value rather than by reference.

`vector1` : | the first GimpVector2.
`vector2` : | the second GimpVector2.
Returns : | The inner product.

### gimp_vector2_cross_product ()

    GimpVector2 gimp_vector2_cross_product      (const GimpVector2 *vector1,
                                                 const GimpVector2 *vector2);

Compute the cross product of two vectors. The result is a GimpVector2 which is orthognal to both `vector1` and `vector2`. If `vector1` and `vector2` are parallel, the result will be the nul vector.

Note that in 2D, this function is useful to test if two vectors are parallel or not, or to compute the area spawned by two vectors.

`vector1` : | a pointer to the first GimpVector2.
`vector2` : | a pointer to the second GimpVector2.
Returns : | The cross product.

### gimp_vector2_cross_product_val ()

    GimpVector2 gimp_vector2_cross_product_val  (GimpVector2 vector1,
                                                 GimpVector2 vector2);

This function is identical to `gimp_vector2_cross_product()` but the vectors are passed by value rather than by reference.

`vector1` : | the first GimpVector2.
`vector2` : | the second GimpVector2.
Returns : | The cross product.

### gimp_vector2_rotate ()

    void        gimp_vector2_rotate             (GimpVector2 *vector,
                                                 gdouble alpha);

Rotates the `vector` counterclockwise by `alpha` radians.

`vector` : | a pointer to a GimpVector2.
`alpha` : | an angle (in radians).

### gimp_vector2_rotate_val ()

    GimpVector2 gimp_vector2_rotate_val         (GimpVector2 vector,
                                                 gdouble alpha);

This function is identical to `gimp_vector2_rotate()` but the vector is passed by value rather than by reference.

`vector` : | a GimpVector2.
`alpha` : | an angle (in radians).
Returns : | a GimpVector2 representing `vector` rotated by `alpha` radians.

### gimp_vector3_new ()

    GimpVector3 gimp_vector3_new                (gdouble x,
                                                 gdouble y,
                                                 gdouble z);

Creates a GimpVector3 of coordinate `x`, `y` and `z`.

`x` : | the X coordinate.
`y` : | the Y coordinate.
`z` : | the Z coordinate.
Returns : | the resulting GimpVector3.

### gimp_vector3_set ()

    void        gimp_vector3_set                (GimpVector3 *vector,
                                                 gdouble x,
                                                 gdouble y,
                                                 gdouble z);

Sets the X, Y and Z coordinates of `vector` to `x`, `y` and `z`.

`vector` : | a pointer to a GimpVector3.
`x` : | the X coordinate.
`y` : | the Y coordinate.
`z` : | the Z coordinate.

### gimp_vector3_length ()

    gdouble     gimp_vector3_length             (const GimpVector3 *vector);

Computes the length of a 3D vector.

`vector` : | a pointer to a GimpVector3.
Returns : | the length of `vector` (a positive gdouble).

### gimp_vector3_length_val ()

    gdouble     gimp_vector3_length_val         (GimpVector3 vector);

This function is identical to `gimp_vector3_length()` but the vector is passed by value rather than by reference.

`vector` : | a GimpVector3.
Returns : | the length of `vector` (a positive gdouble).

### gimp_vector3_mul ()

    void        gimp_vector3_mul                (GimpVector3 *vector,
                                                 gdouble factor);

Multiplies each component of the `vector` by `factor`. Note that this is equivalent to multiplying the vectors length by `factor`.

`vector` : | a pointer to a GimpVector3.
`factor` : | a scalar.

### gimp_vector3_mul_val ()

    GimpVector3 gimp_vector3_mul_val            (GimpVector3 vector,
                                                 gdouble factor);

This function is identical to `gimp_vector3_mul()` but the vector is passed by value rather than by reference.

`vector` : | a GimpVector3.
`factor` : | a scalar.
Returns : | the resulting GimpVector3.

### gimp_vector3_normalize ()

    void        gimp_vector3_normalize          (GimpVector3 *vector);

Normalizes the `vector` so the length of the `vector` is 1.0. The nul vector will not be changed.

`vector` : | a pointer to a GimpVector3.

### gimp_vector3_normalize_val ()

    GimpVector3 gimp_vector3_normalize_val      (GimpVector3 vector);

This function is identical to `gimp_vector3_normalize()` but the vector is passed by value rather than by reference.

`vector` : | a GimpVector3.
Returns : | a GimpVector3 parallel to `vector`, pointing in the same direction but with a length of 1.0.

### gimp_vector3_neg ()

    void        gimp_vector3_neg                (GimpVector3 *vector);

Negates the `vector` (i.e. negate all its coordinates).

`vector` : | a pointer to a GimpVector3.

### gimp_vector3_neg_val ()

    GimpVector3 gimp_vector3_neg_val            (GimpVector3 vector);

This function is identical to `gimp_vector3_neg()` but the vector is passed by value rather than by reference.

`vector` : | a GimpVector3.
Returns : | the negated GimpVector3.

### gimp_vector3_add ()

    void        gimp_vector3_add                (GimpVector3 *result,
                                                 const GimpVector3 *vector1,
                                                 const GimpVector3 *vector2);

Computes the sum of two 3D vectors. The resulting GimpVector3 is stored in `result`.

`result` : | destination for the resulting GimpVector3.
`vector1` : | a pointer to the first GimpVector3.
`vector2` : | a pointer to the second GimpVector3.

### gimp_vector3_add_val ()

    GimpVector3 gimp_vector3_add_val            (GimpVector3 vector1,
                                                 GimpVector3 vector2);

This function is identical to `gimp_vector3_add()` but the vectors are passed by value rather than by reference.

`vector1` : | a GimpVector3.
`vector2` : | a GimpVector3.
Returns : | the resulting GimpVector3.

### gimp_vector3_sub ()

    void        gimp_vector3_sub                (GimpVector3 *result,
                                                 const GimpVector3 *vector1,
                                                 const GimpVector3 *vector2);

Computes the difference of two 3D vectors (`vector1` minus `vector2`). The resulting GimpVector3 is stored in `result`.

`result` : | the destination for the resulting GimpVector3.
`vector1` : | a pointer to the first GimpVector3.
`vector2` : | a pointer to the second GimpVector3.

### gimp_vector3_sub_val ()

    GimpVector3 gimp_vector3_sub_val            (GimpVector3 vector1,
                                                 GimpVector3 vector2);

This function is identical to `gimp_vector3_sub()` but the vectors are passed by value rather than by reference.

`vector1` : | a GimpVector3.
`vector2` : | a GimpVector3.
Returns : | the resulting GimpVector3.

### gimp_vector3_inner_product ()

    gdouble     gimp_vector3_inner_product      (const GimpVector3 *vector1,
                                                 const GimpVector3 *vector2);

Computes the inner (dot) product of two 3D vectors. This product is zero if and only if the two vectors are orthognal.

`vector1` : | a pointer to the first GimpVector3.
`vector2` : | a pointer to the second GimpVector3.
Returns : | The inner product.

### gimp_vector3_inner_product_val ()

    gdouble     gimp_vector3_inner_product_val  (GimpVector3 vector1,
                                                 GimpVector3 vector2);

This function is identical to `gimp_vector3_inner_product()` but the vectors are passed by value rather than by reference.

`vector1` : | the first GimpVector3.
`vector2` : | the second GimpVector3.
Returns : | The inner product.

### gimp_vector3_cross_product ()

    GimpVector3 gimp_vector3_cross_product      (const GimpVector3 *vector1,
                                                 const GimpVector3 *vector2);

Compute the cross product of two vectors. The result is a GimpVector3 which is orthognal to both `vector1` and `vector2`. If `vector1` and `vector2` and parallel, the result will be the nul vector.

This function can be used to compute the normal of the plane defined by `vector1` and `vector2`.

`vector1` : | a pointer to the first GimpVector3.
`vector2` : | a pointer to the second GimpVector3.
Returns : | The cross product.

### gimp_vector3_cross_product_val ()

    GimpVector3 gimp_vector3_cross_product_val  (GimpVector3 vector1,
                                                 GimpVector3 vector2);

This function is identical to `gimp_vector3_cross_product()` but the vectors are passed by value rather than by reference.

`vector1` : | the first GimpVector3.
`vector2` : | the second GimpVector3.
Returns : | The cross product.

### gimp_vector3_rotate ()

    void        gimp_vector3_rotate             (GimpVector3 *vector,
                                                 gdouble alpha,
                                                 gdouble beta,
                                                 gdouble gamma);

Rotates the `vector` around the three axis (Z, Y, and X) by `alpha`, `beta` and `gamma`, respectively.

Note that the order of the rotation is very important. If you expect a vector to be rotated around X, and then around Y, you will have to call this function twice. Also, it is often wise to call this function with only one of `alpha`, `beta` and `gamma` non-zero.

`vector` : | a pointer to a GimpVector3.
`alpha` : | the angle (in radian) of rotation around the Z axis.
`beta` : | the angle (in radian) of rotation around the Y axis.
`gamma` : | the angle (in radian) of rotation around the X axis.

### gimp_vector3_rotate_val ()

    GimpVector3 gimp_vector3_rotate_val         (GimpVector3 vector,
                                                 gdouble alpha,
                                                 gdouble beta,
                                                 gdouble gamma);

This function is identical to `gimp_vector3_rotate()` but the vectors are passed by value rather than by reference.

`vector` : | a GimpVector3.
`alpha` : | the angle (in radian) of rotation around the Z axis.
`beta` : | the angle (in radian) of rotation around the Y axis.
`gamma` : | the angle (in radian) of rotation around the X axis.
Returns : | the rotated vector.

### gimp_vector_2d_to_3d ()

    void        gimp_vector_2d_to_3d            (gint sx,
                                                 gint sy,
                                                 gint w,
                                                 gint h,
                                                 gint x,
                                                 gint y,
                                                 const GimpVector3 *vp,
                                                 GimpVector3 *p);

\"Compute screen (sx, sy) - (sx + w, sy + h) to 3D unit square mapping. The plane to map to is given in the z field of p. The observer is located at position vp (vp->z != 0.0).\"

In other words, this computes the projection of the point (`x`, `y`) to the plane z = `p->z` (parallel to XY), from the `vp` point of view through the screen (`sx`, `sy`)->(`sx` + `w`, `sy` + `h`)

`sx` : | the abscisse of the upper-left screen rectangle.
`sy` : | the ordinate of the upper-left screen rectangle.
`w` : | the width of the screen rectangle.
`h` : | the height of the screen rectangle.
`x` : | the abscisse of the point in the screen rectangle to map.
`y` : | the ordinate of the point in the screen rectangle to map.
`vp` : | the position of the observer.
`p` : | the resulting point.

### gimp_vector_2d_to_3d_val ()

    GimpVector3 gimp_vector_2d_to_3d_val        (gint sx,
                                                 gint sy,
                                                 gint w,
                                                 gint h,
                                                 gint x,
                                                 gint y,
                                                 GimpVector3 vp,
                                                 GimpVector3 p);

This function is identical to `gimp_vector_2d_to_3d()` but the position of the `observer` and the resulting point `p` are passed by value rather than by reference.

`sx` : | the abscisse of the upper-left screen rectangle.
`sy` : | the ordinate of the upper-left screen rectangle.
`w` : | the width of the screen rectangle.
`h` : | the height of the screen rectangle.
`x` : | the abscisse of the point in the screen rectangle to map.
`y` : | the ordinate of the point in the screen rectangle to map.
`vp` : | position of the observer.
`p` : | the resulting point.
Returns : | the computed GimpVector3 point.

### gimp_vector_3d_to_2d ()

    void        gimp_vector_3d_to_2d            (gint sx,
                                                 gint sy,
                                                 gint w,
                                                 gint h,
                                                 gdouble *x,
                                                 gdouble *y,
                                                 const GimpVector3 *vp,
                                                 const GimpVector3 *p);

Convert the given 3D point to 2D (project it onto the viewing plane, (sx, sy, 0) - (sx + w, sy + h, 0). The input is assumed to be in the unit square (0, 0, z) - (1, 1, z). The viewpoint of the observer is passed in vp.

This is basically the opposite of `gimp_vector_2d_to_3d()`.

`sx` : | the abscisse of the upper-left screen rectangle.
`sy` : | the ordinate of the upper-left screen rectangle.
`w` : | the width of the screen rectangle.
`h` : | the height of the screen rectangle.
`x` : | the abscisse of the point in the screen rectangle to map (return value).
`y` : | the ordinate of the point in the screen rectangle to map (return value).
`vp` : | position of the observer.
`p` : | the 3D point to project to the plane.

## See Also

GimpMatrix3

GimpMatrix4