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# Math
We obviously need to deal with lots of points, rectangles, and transformations
in MuPDF.
## fz_point
Points are fairly self evident. The `fz_make_point` utility function is for use
with Visual Studio that doesn't yet support the C99 struct initializer syntax.
typedef struct {
float x, y;
} fz_point;
fz_point fz_make_point(float x, float y);
## fz_rect and fz_irect
Rectangles are represented by two pairs of coordinates. The `x0`, `y0` pair
have the smallest values, and in the normal coordinate space used by MuPDF that
is the upper left corner. The `x1`, `y1` pair have the largest values,
typically the lower right corner.
In order to represent an infinite unbounded area, we use an `x0` that is larger
than the `x1`.
typedef struct {
float x0, y0;
float x1, y1;
} fz_rect;
const fz_rect fz_infinite_rect = { 1, 1, -1, -1 };
const fz_rect fz_empty_rect = { 0, 0, 0, 0 };
const fz_rect fz_unit_rect = { 0, 0, 1, 1 };
fz_rect fz_make_rect(float x0, float y0, float x1, float y1);
## fz_matrix
Our matrix structure is a row-major 3x3 matrix with the last column always
`[ 0 0 1 ]`. This is represented as a struct with six fields, in the same order as
in PDF and Postscript. The identity matrix is a global constant, for easy
access.
/ a b 0 \
| c d 0 |
\ e f 1 /
typedef struct {
float a, b, c, d, e, f;
} fz_matrix;
const fz_matrix fz_identity = { 1, 0, 0, 1, 0, 0 };
fz_matrix fz_make_matrix(float a, float b, float c, float d, float e, float f);
## fz_quad
Sometimes we need to represent a non-axis aligned rectangular-ish area, such as
the area covered by some rotated text. For this we use a quad representation,
using a points for each of the upper/lower/left/right corners as seen from the
reading direction of the text represented.
typedef struct {
fz_point ul, ur, ll, lr;
} fz_quad;
## List of math functions
These are simple mathematical operations that can not throw errors, so do not need a context argument.
`float fz_abs(float f)`
: Abs for float.
`float fz_min(float a, float b)`
: Min for float.
`float fz_max(float a, float b)`
: Max for float.
`float fz_clamp(float f, float min, float max)`
: Clamp for float.
`int fz_absi(int i)`
: Abs for integer.
`int fz_mini(int a, int b)`
: Min for integer.
`int fz_maxi(int a, int b)`
: Max for integer.
`int fz_clampi(int i, int min, int max)`
: Clamp for integer.
`int fz_is_empty_rect(fz_rect r)`
: Returns whether the supplied `fz_rect` is empty.
`int fz_is_infinite_rect(fz_rect r)`
: Returns whether the supplied `fz_rect` is infinite.
`fz_matrix fz_concat(fz_matrix left, fz_matrix right)`
: Concat two matrices and returns a new matrix.
`fz_matrix fz_scale(float sx, float sy)`
: Scale.
`fz_matrix fz_shear(float sx, float sy)`
: Shear.
`fz_matrix fz_rotate(float degrees)`
: Rotate.
`fz_matrix fz_translate(float tx, float ty)`
: Translate.
`fz_matrix fz_invert_matrix(fz_matrix matrix)`
: Invert a matrix.
`fz_point fz_transform_point(fz_point point, fz_matrix m)`
: Transform a point according to the given matrix.
`fz_point fz_transform_vector(fz_point vector, fz_matrix m)`
: Transform a vector according to the given matrix (ignores translation).
`fz_rect fz_transform_rect(fz_rect rect, fz_matrix m)`
: Transform a `fz_rect` according to the given matrix.
`fz_quad fz_transform_quad(fz_quad q, fz_matrix m)`
: Transform a `fz_quad` according to the given matrix.
`int fz_is_point_inside_rect(fz_point p, fz_rect r)`
: Returns whether the point is inside the supplied `fz_rect`.
`int fz_is_point_inside_quad(fz_point p, fz_quad q)`
: Returns whether the point is inside the supplied `fz_quad`.
`fz_matrix fz_transform_page(fz_rect mediabox, float resolution, float rotate)`
: Create a transform matrix to draw a page at a given resolution and
rotation. The scaling factors are adjusted so that the page covers a
whole number of pixels. Resolution is given in dots per inch. Rotation
is expressed in 90 degree increments (`0`, `90`, `180`, and `270` are
valid values).
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