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ADD: MuPDF v1.26.7: the MuPDF source as downloaded by a default build of PyMuPDF 1.26.4. The directory name has changed: no version number in the expanded directory now.
author Franz Glasner <fzglas.hg@dom66.de>
date Mon, 15 Sep 2025 11:43:07 +0200
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1 # Math
2
3 We obviously need to deal with lots of points, rectangles, and transformations
4 in MuPDF.
5
6 ## fz_point
7
8 Points are fairly self evident. The `fz_make_point` utility function is for use
9 with Visual Studio that doesn't yet support the C99 struct initializer syntax.
10
11 typedef struct {
12 float x, y;
13 } fz_point;
14
15 fz_point fz_make_point(float x, float y);
16
17 ## fz_rect and fz_irect
18
19 Rectangles are represented by two pairs of coordinates. The `x0`, `y0` pair
20 have the smallest values, and in the normal coordinate space used by MuPDF that
21 is the upper left corner. The `x1`, `y1` pair have the largest values,
22 typically the lower right corner.
23
24 In order to represent an infinite unbounded area, we use an `x0` that is larger
25 than the `x1`.
26
27 typedef struct {
28 float x0, y0;
29 float x1, y1;
30 } fz_rect;
31
32 const fz_rect fz_infinite_rect = { 1, 1, -1, -1 };
33 const fz_rect fz_empty_rect = { 0, 0, 0, 0 };
34 const fz_rect fz_unit_rect = { 0, 0, 1, 1 };
35
36 fz_rect fz_make_rect(float x0, float y0, float x1, float y1);
37
38 ## fz_matrix
39
40 Our matrix structure is a row-major 3x3 matrix with the last column always
41 `[ 0 0 1 ]`. This is represented as a struct with six fields, in the same order as
42 in PDF and Postscript. The identity matrix is a global constant, for easy
43 access.
44
45 / a b 0 \
46 | c d 0 |
47 \ e f 1 /
48
49 typedef struct {
50 float a, b, c, d, e, f;
51 } fz_matrix;
52
53 const fz_matrix fz_identity = { 1, 0, 0, 1, 0, 0 };
54
55 fz_matrix fz_make_matrix(float a, float b, float c, float d, float e, float f);
56
57 ## fz_quad
58
59 Sometimes we need to represent a non-axis aligned rectangular-ish area, such as
60 the area covered by some rotated text. For this we use a quad representation,
61 using a points for each of the upper/lower/left/right corners as seen from the
62 reading direction of the text represented.
63
64 typedef struct {
65 fz_point ul, ur, ll, lr;
66 } fz_quad;
67
68 ## List of math functions
69
70 These are simple mathematical operations that can not throw errors, so do not need a context argument.
71
72 `float fz_abs(float f)`
73 : Abs for float.
74
75 `float fz_min(float a, float b)`
76 : Min for float.
77
78 `float fz_max(float a, float b)`
79 : Max for float.
80
81 `float fz_clamp(float f, float min, float max)`
82 : Clamp for float.
83
84 `int fz_absi(int i)`
85 : Abs for integer.
86
87 `int fz_mini(int a, int b)`
88 : Min for integer.
89
90 `int fz_maxi(int a, int b)`
91 : Max for integer.
92
93 `int fz_clampi(int i, int min, int max)`
94 : Clamp for integer.
95
96 `int fz_is_empty_rect(fz_rect r)`
97 : Returns whether the supplied `fz_rect` is empty.
98
99 `int fz_is_infinite_rect(fz_rect r)`
100 : Returns whether the supplied `fz_rect` is infinite.
101
102 `fz_matrix fz_concat(fz_matrix left, fz_matrix right)`
103 : Concat two matrices and returns a new matrix.
104
105 `fz_matrix fz_scale(float sx, float sy)`
106 : Scale.
107
108 `fz_matrix fz_shear(float sx, float sy)`
109 : Shear.
110
111 `fz_matrix fz_rotate(float degrees)`
112 : Rotate.
113
114 `fz_matrix fz_translate(float tx, float ty)`
115 : Translate.
116
117 `fz_matrix fz_invert_matrix(fz_matrix matrix)`
118 : Invert a matrix.
119
120 `fz_point fz_transform_point(fz_point point, fz_matrix m)`
121 : Transform a point according to the given matrix.
122
123 `fz_point fz_transform_vector(fz_point vector, fz_matrix m)`
124 : Transform a vector according to the given matrix (ignores translation).
125
126 `fz_rect fz_transform_rect(fz_rect rect, fz_matrix m)`
127 : Transform a `fz_rect` according to the given matrix.
128
129 `fz_quad fz_transform_quad(fz_quad q, fz_matrix m)`
130 : Transform a `fz_quad` according to the given matrix.
131
132 `int fz_is_point_inside_rect(fz_point p, fz_rect r)`
133 : Returns whether the point is inside the supplied `fz_rect`.
134
135 `int fz_is_point_inside_quad(fz_point p, fz_quad q)`
136 : Returns whether the point is inside the supplied `fz_quad`.
137
138 `fz_matrix fz_transform_page(fz_rect mediabox, float resolution, float rotate)`
139 : Create a transform matrix to draw a page at a given resolution and
140 rotation. The scaling factors are adjusted so that the page covers a
141 whole number of pixels. Resolution is given in dots per inch. Rotation
142 is expressed in 90 degree increments (`0`, `90`, `180`, and `270` are
143 valid values).