tikra 1.2.0

TikZ figures to SVG and PNG with no TeX install; math labels by mathra.
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248

//! Polar axes (`tikzlibrarypgfplots.polar.code.tex`): x is an angle in degrees, y a radius. The
//! axis is a circle (or a sector from `xmin` to `xmax`), from 0 or `ymin` out to the largest
//! radius, stretched to `width` × `height` (equal by default). Angles tick every 90, 45, 30, 15, 10
//! or 5 degrees (`…normalizetickdist@polar`), the last tick of a full circle is the first one;
//! the grid is rays and arcs, the tick labels sit outside the circle and along the first ray.

use std::f64::consts::PI;

use crate::scene::{Point, Segment};
use crate::{Error, PT};

use super::super::nodes::{NodeSpec, OnPath};
use super::draw::{axis_char, tick_offset, visible, Frame, Setup};
use super::keys;
use super::{toks, Engine};

/// sin and cos of degrees, exact at multiples of 90.
pub fn sin_cos(deg: f64) -> (f64, f64) {
    let r = deg.rem_euclid(360.0);
    if r == 0.0 {
        (0.0, 1.0)
    } else if r == 90.0 {
        (1.0, 0.0)
    } else if r == 180.0 {
        (0.0, -1.0)
    } else if r == 270.0 {
        (-1.0, 0.0)
    } else {
        deg.to_radians().sin_cos()
    }
}

/// Whether [xmin, xmax] is a whole turn (`\pgfplots@xtick@disable@last@tick`).
fn full(xmin: f64, xmax: f64) -> bool {
    let d = (xmax - xmin).rem_euclid(360.0);
    d.abs() < 0.002 || (360.0 - d).abs() < 0.002
}

/// Points of the sector's outline, in units of the data (radius), for its size.
fn outline_points(xmin: f64, xmax: f64, ymin: f64, ymax: f64) -> Vec<(f64, f64)> {
    let mut v = Vec::new();
    let steps = (((xmax - xmin).abs() * 2.0).ceil() as usize).clamp(4, 2000);
    for k in 0..=steps {
        let a = xmin + (xmax - xmin) * k as f64 / steps as f64;
        let (s, c) = sin_cos(a);
        v.push((ymax * c, ymax * s));
        v.push((ymin * c, ymin * s));
    }
    v
}

/// Whether a point of the canvas lies in the sector (`\pgfplotsaxisifcontainspoint@polar`): its
/// radius within [ymin, ymax] and its angle, modulo 360, within [xmin, xmax].
pub fn contains(f: &Frame, p: Point) -> bool {
    let d = p.minus(f.origin);
    let (u, v) = (d.x / f.e[0].x, d.y / f.e[1].y);
    if !(u.is_finite() && v.is_finite()) {
        return true;
    }
    let tol = 0.05 * PT / f.e[1].norm().max(1e-12);
    let r = u.hypot(v);
    if r < f.min[1].abs().min(f.max[1].abs()) - tol || r > f.max[1].abs() + tol {
        return false;
    }
    if r <= tol || full(f.min[0], f.max[0]) {
        return true;
    }
    let a = v.atan2(u).to_degrees().rem_euclid(360.0);
    let (lo, hi) = (f.min[0].rem_euclid(360.0), f.max[0].rem_euclid(360.0));
    let eps = 1e-3;
    if hi > lo {
        a >= lo - eps && a <= hi + eps
    } else {
        // the sector goes round 0
        a <= hi + eps || a >= lo - eps
    }
}

/// The sector's outline on the canvas.
pub fn outline(f: &Frame) -> Vec<Point> {
    outline_points(f.min[0], f.max[0], f.min[1], f.max[1]).into_iter().map(|(x, y)| f.origin.plus(f.e[0].scale(x)).plus(f.e[1].scale(y))).collect()
}

/// An arc of radius `r` from angle `a0` to `a1`, as Bézier pieces of at most 90°.
fn arc(f: &Frame, r: f64, a0: f64, a1: f64, segs: &mut Vec<Segment>, start: bool) {
    let map = |u: f64, v: f64| f.origin.plus(f.e[0].scale(u)).plus(f.e[1].scale(v));
    let n = ((a1 - a0).abs() / 90.0).ceil().max(1.0) as usize;
    let step = (a1 - a0) / n as f64;
    let (s0, c0) = sin_cos(a0);
    if start {
        segs.push(Segment::MoveTo(map(r * c0, r * s0)));
    }
    for i in 0..n {
        let (t0, t1) = (a0 + step * i as f64, a0 + step * (i + 1) as f64);
        let k = 4.0 / 3.0 * ((t1 - t0).to_radians() / 4.0).tan();
        let ((s0, c0), (s1, c1)) = (sin_cos(t0), sin_cos(t1));
        let p1 = map(r * (c0 - k * s0), r * (s0 + k * c0));
        let p2 = map(r * (c1 + k * s1), r * (s1 - k * c1));
        segs.push(Segment::CurveTo(p1, p2, map(r * c1, r * s1)));
    }
}

/// The clip path: the sector (`\pgfplots@clippath@prepare@for@axistype@polaraxis`).
pub fn clip_path(f: &Frame) -> Vec<Segment> {
    let (xmin, xmax, ymin, ymax) = (f.min[0], f.max[0], f.min[1], f.max[1]);
    let mut segs = Vec::new();
    arc(f, ymax, xmin, xmax, &mut segs, true);
    if full(xmin, xmax) {
        if ymin != 0.0 {
            arc(f, ymin, xmin, xmax, &mut segs, true);
        }
    } else if ymin == 0.0 {
        segs.push(Segment::LineTo(f.origin));
    } else {
        let (s, c) = sin_cos(xmax);
        segs.push(Segment::LineTo(f.origin.plus(f.e[0].scale(ymin * c)).plus(f.e[1].scale(ymin * s))));
        arc(f, ymin, xmax, xmin, &mut segs, false);
    }
    segs.push(Segment::Close);
    segs
}

/// The angles' ticks; None for the radius (it ticks as a linear axis).
pub fn ticks(e: &mut Engine, a: usize, f: &Frame) -> Option<(Vec<f64>, f64)> {
    if a != 0 {
        return None;
    }
    // given ticks are read as usual
    let raw = crate::keys::value(&e.tex, "/pgfplots/xtick").unwrap_or_default();
    if !crate::keys::trim(&raw).is_empty() || keys::number(e, "/pgfplots/xtick distance").is_some() {
        return None;
    }
    let (xmin, xmax) = (f.min[0], f.max[0]);
    // the circumference (`\pgfplotspointxaxislength`)
    let mut length = f.e[0].norm() * f.max[1] * 2.0 * PI / PT;
    let frac = (xmax - xmin) / 360.0;
    if frac < 1.0 {
        length *= frac;
    }
    let max_space = keys::number(e, "/pgfplots/max space between ticks").unwrap_or(35.0);
    let try_min = keys::number(e, "/pgfplots/try min ticks").unwrap_or(4.0) as usize;
    let n = ((length / max_space).floor() as usize + 1).max(try_min);
    // H = (MAX + 0.001pt - MIN) / (n-1), as TeX divides
    let sp = |v: f64| (v * 65536.0).round();
    let h = ((sp(xmax) + sp(0.001) - sp(xmin)) / (n.max(2) - 1) as f64).trunc() / 65536.0;
    let h = match h {
        h if h > 67.0 => 90.0,
        h if h > 30.0 => 45.0,
        h if h > 18.0 => 30.0,
        h if h > 10.0 => 15.0,
        h if h > 6.0 => 10.0,
        _ => 5.0,
    };
    let settings = super::ticks::TickSettings { length_pt: length, max_space, try_min, distance: Some(h), scale: None };
    let (mut list, d) = super::ticks::linear(xmin, xmax, settings);
    // a whole turn: the last tick is the first
    if full(xmin, xmax) {
        list.retain(|t| (t - xmax).abs() > 1e-6 * h);
    }
    Some((list, d))
}

/// The polar axis: grid, ticks, axis lines and tick labels.
pub(super) fn draw_axis(e: &mut Engine, s: &Setup) -> Result<(), Error> {
    let f = s.frame.clone();
    let (xmin, xmax, ymin, ymax) = (f.min[0], f.max[0], f.min[1], f.max[1]);
    let xt: Vec<f64> = if s.hide[0] { Vec::new() } else { visible(&f, 0, &s.ticks[0]).into_iter().map(|(_, t)| t).collect() };
    let yt: Vec<f64> = if s.hide[1] { Vec::new() } else { visible(&f, 1, &s.ticks[1]).into_iter().map(|(_, t)| t).collect() };
    // grid: rays at the angles, arcs at the radii
    if keys::flag(e, "/pgfplots/xmajorgrids") {
        let segs: Vec<Segment> = xt.iter().flat_map(|t| [Segment::MoveTo(f.at([*t, ymin, 0.0])), Segment::LineTo(f.at([*t, ymax, 0.0]))]).collect();
        e.draw_with("/pgfplots/every axis grid,/pgfplots/every major grid,/pgfplots/every axis x grid,/pgfplots/every major x grid", segs)?;
    }
    if keys::flag(e, "/pgfplots/ymajorgrids") {
        let mut segs = Vec::new();
        for t in &yt {
            arc(&f, *t, xmin, xmax, &mut segs, true);
        }
        e.draw_with("/pgfplots/every axis grid,/pgfplots/every major grid,/pgfplots/every axis y grid,/pgfplots/every major y grid", segs)?;
    }
    // axis lines: the arcs at ymin and ymax, the rays at xmin and xmax
    let mut segs = Vec::new();
    arc(&f, ymax, xmin, xmax, &mut segs, true);
    if ymin > 0.0 {
        arc(&f, ymin, xmin, xmax, &mut segs, true);
    }
    if !s.hide[0] {
        e.draw_with("/pgfplots/every outer x axis line", segs)?;
    }
    if !s.hide[1] {
        let mut segs = Vec::new();
        for a in [xmin, xmax] {
            segs.push(Segment::MoveTo(f.at([a, ymin, 0.0])));
            segs.push(Segment::LineTo(f.at([a, ymax, 0.0])));
        }
        e.draw_with("/pgfplots/every outer y axis line", segs)?;
    }
    // tick labels: angles outside the circle, radii along the first ray
    for (a, list) in [(0usize, &xt), (1usize, &yt)] {
        if s.hide[a] || !keys::flag(e, &format!("/pgfplots/{}majorticks", axis_char(a))) {
            continue;
        }
        let c = axis_char(a);
        let styles = format!("/pgfplots/every tick label,/pgfplots/every {c} tick label");
        let off = tick_offset(e, a);
        let sloped = match e.tex.meaning_of(&crate::keys::macro_name(&format!("/pgfplots/every {c} tick label/.@cmd"))) {
            crate::tex::Meaning::Macro(m) => crate::tex::tokens_to_string(&crate::tex::substitute(&m.body, &[])).contains("sloped"),
            _ => false,
        };
        for (k, t) in list.iter().enumerate() {
            let (p, out) = if a == 0 {
                let p = f.at([*t, ymax, 0.0]);
                (p, super::draw::unit(p.minus(f.origin)))
            } else {
                let (sn, cs) = sin_cos(xmin);
                let n = super::draw::unit(f.e[0].scale(-sn).plus(f.e[1].scale(cs)));
                (f.at([xmin, *t, 0.0]), n)
            };
            let at = p.plus(out.scale(off));
            let shown = if a == 0 && *t > 360.0 { t.rem_euclid(360.0) } else { *t };
            e.begin_group();
            let r = (|| {
                e.keys_tikz(&styles)?;
                super::draw::tick_text_for(e, a, shown, k)
            })();
            e.end_group();
            let text = r?;
            // the node's border faces the axis: an angle anchor against the outward direction
            let mut angle = (-out.y).atan2(-out.x).to_degrees();
            // `sloped like x axis` turns an angle's label along the circle, never upside down:
            // the anchor turns with it
            if a == 0 && sloped {
                let (sn, cs) = sin_cos(*t);
                let mut d = f.e[0].scale(-sn).plus(f.e[1].scale(cs));
                if d.x < 0.0 {
                    d = d.scale(-1.0);
                }
                angle -= d.y.atan2(d.x).to_degrees();
                f.slope.set(Some(d));
            }
            let options = toks(&format!("anchor={angle},{styles}"));
            let items = e.node(NodeSpec { options, name: None, at: Some(at), text, place: OnPath::Point(at), point: at, coordinate: false, default_pos: None });
            f.slope.set(None);
            e.canvas.items.extend(items?);
        }
    }
    Ok(())
}