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).