WIP

src/axis.typ

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+
+/// Transform linear axis value to linear space (low, high)
+#let _transform-lin(ax, value, low, high) = {
+  let range = high - low
+
+  return (value - ax.low) * (range / (ax.high - ax.low))
+}
+
+/// Transform log axis value to linear space (low, high)
+#let _transform-log(ax, value, low, high) = {
+  let range = high - low
+
+  let f(x) = {
+    calc.log(calc.max(x, util.float-epsilon), base: ax.base)
+  }
+
+  return (value - f(ax.low)) * (range / (f(ax.high) - f(ax.low)))
+}
+
+#let linear(low, high) = (
+  low: low, high: high, transform: _transform-lin,
+)
+
+#let logarithmic(low, high, base) = (
+  low: low, high: high, base: base, transform: _transform-log,
+)
+
+/// Transform an axis value to a linear value between low and high
+/// - ax (axis): Axis
+/// - value (number): Value to transform from axis space to linear space
+/// - low (number): Linear minimum
+/// - high (number): Linear maximum
+#let transform(ax, value, low, high) = {
+  return (ax.transform)(ax, value, low, high)
+}

src/projection.typ

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+
+/// Create a new cartesian projection between two vectors, low and high
+///
+/// - low (vector): Low vector
+/// - high (vector): High vector
+/// - x (axis): X axis
+/// - y (axis): Y axis
+/// - z (axis): Z axis
+/// -> function Transformation for one or more vectors
+#let cartesian(low, high, x, y, z) = {
+  let axes = (x, y, z)
+
+  return (..v) = {
+    return v.pos().map(v => {
+      for i range(0, v.len()) {
+        v.at(i) = (axes.at(i).transform)(axes.at(i), v.at(i), low.at(i), high.at(i))
+      }
+    })
+  }
+}
+
+/// - center (vector): Center vector
+/// - start (angle): Start angle (0deg for full circle)
+/// - stop (angle): Stop angle (360deg for full circle)
+/// - theta (axis): Theta axis
+/// - r (axis): R axis
+/// -> function Transformation for one or more vectors
+#let polar(center, radius, start, stop, theta, r) = {
+  return (..v) => {
+    let v = v.pos()
+    // TODO
+    return v
+  }
+}

src/ticks.typ

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+// Compute list of linear ticks for axis
+//
+// - axis (axis): Axis
+#let compute-linear-ticks(axis, style, add-zero: true) = {
+  let (min, max) = (axis.min, axis.max)
+  let dt = max - min; if (dt == 0) { dt = 1 }
+  let ticks = axis.ticks
+  let ferr = util.float-epsilon
+  let tick-limit = style.tick-limit
+  let minor-tick-limit = style.minor-tick-limit
+
+  let l = ()
+  if ticks != none {
+    let major-tick-values = ()
+    if "step" in ticks and ticks.step != none {
+      assert(ticks.step >= 0,
+             message: "Axis tick step must be positive and non 0.")
+      if axis.min > axis.max { ticks.step *= -1 }
+
+      let s = 1 / ticks.step
+
+      let num-ticks = int(max * s + 1.5)  - int(min * s)
+      assert(num-ticks <= tick-limit,
+             message: "Number of major ticks exceeds limit " + str(tick-limit))
+
+      let n = range(int(min * s), int(max * s + 1.5))
+      for t in n {
+        let v = (t / s - min) / dt
+        if t / s == 0 and not add-zero { continue }
+
+        if v >= 0 - ferr and v <= 1 + ferr {
+          l.push((v, format-tick-value(t / s, ticks), true))
+          major-tick-values.push(v)
+        }
+      }
+    }
+
+    if "minor-step" in ticks and ticks.minor-step != none {
+      assert(ticks.minor-step >= 0,
+             message: "Axis minor tick step must be positive")
+      if axis.min > axis.max { ticks.minor-step *= -1 }
+
+      let s = 1 / ticks.minor-step
+
+      let num-ticks = int(max * s + 1.5) - int(min * s)
+      assert(num-ticks <= minor-tick-limit,
+             message: "Number of minor ticks exceeds limit " + str(minor-tick-limit))
+
+      let n = range(int(min * s), int(max * s + 1.5))
+      for t in n {
+        let v = (t / s - min) / dt
+        if v in major-tick-values {
+          // Prefer major ticks over minor ticks
+          continue
+        }
+
+        if v != none and v >= 0 and v <= 1 + ferr {
+          l.push((v, none, false))
+        }
+      }
+    }
+
+  }
+
+  return l
+}
+
+// Compute list of linear ticks for axis
+//
+// - axis (axis): Axis
+#let compute-logarithmic-ticks(axis, style, add-zero: true) = {
+  let ferr = util.float-epsilon
+  let (min, max) = (
+    calc.log(calc.max(axis.min, ferr), base: axis.base),
+    calc.log(calc.max(axis.max, ferr), base: axis.base)
+  )
+  let dt = max - min; if (dt == 0) { dt = 1 }
+  let ticks = axis.ticks
+
+  let tick-limit = style.tick-limit
+  let minor-tick-limit = style.minor-tick-limit
+  let l = ()
+
+  if ticks != none {
+    let major-tick-values = ()
+    if "step" in ticks and ticks.step != none {
+      assert(ticks.step >= 0,
+             message: "Axis tick step must be positive and non 0.")
+      if axis.min > axis.max { ticks.step *= -1 }
+
+      let s = 1 / ticks.step
+
+      let num-ticks = int(max * s + 1.5)  - int(min * s)
+      assert(num-ticks <= tick-limit,
+             message: "Number of major ticks exceeds limit " + str(tick-limit))
+
+      let n = range(
+        int(min * s),
+        int(max * s + 1.5)
+      )
+
+      for t in n {
+        let v = (t / s - min) / dt
+        if t / s == 0 and not add-zero { continue }
+
+        if v >= 0 - ferr and v <= 1 + ferr {
+          l.push((v, format-tick-value( calc.pow(axis.base, t / s), ticks), true))
+          major-tick-values.push(v)
+        }
+      }
+    }
+
+    if "minor-step" in ticks and ticks.minor-step != none {
+      assert(ticks.minor-step >= 0,
+             message: "Axis minor tick step must be positive")
+      if axis.min > axis.max { ticks.minor-step *= -1 }
+
+      let s = 1 / ticks.step
+      let n = range(int(min * s)-1, int(max * s + 1.5)+1)
+
+      for t in n {
+        for vv in range(1, int(axis.base / ticks.minor-step)) {
+
+          let v = ( (calc.log(vv * ticks.minor-step, base: axis.base) + t)/ s - min) / dt
+          if v in major-tick-values {continue}
+
+          if v != none and v >= 0 and v <= 1 + ferr {
+            l.push((v, none, false))
+          }
+
+        }
+
+      }
+    }
+  }
+
+  return l
+}
+
+// Get list of fixed axis ticks
+//
+// - axis (axis): Axis object
+#let fixed-ticks(axis) = {
+  let l = ()
+  if "list" in axis.ticks {
+    for t in axis.ticks.list {
+      let (v, label) = (none, none)
+      if type(t) in (float, int) {
+        v = t
+        label = format-tick-value(t, axis.ticks)
+      } else {
+        (v, label) = t
+      }
+
+      v = value-on-axis(axis, v)
+      if v != none and v >= 0 and v <= 1 {
+        l.push((v, label, true))
+      }
+    }
+  }
+  return l
+}
+
+// Compute list of axis ticks
+//
+// A tick triple has the format:
+//   (rel-value: float, label: content, major: bool)
+//
+// - axis (axis): Axis object
+#let compute-ticks(axis, style, add-zero: true) = {
+  let find-max-n-ticks(axis, n: 11) = {
+    let dt = calc.abs(axis.max - axis.min)
+    let scale = calc.floor(calc.log(dt, base: 10) - 1)
+    if scale > 5 or scale < -5 {return none}
+
+    let (step, best) = (none, 0)
+    for s in style.auto-tick-factors {
+      s = s * calc.pow(10, scale)
+
+      let divs = calc.abs(dt / s)
+      if divs >= best and divs <= n {
+        step = s
+        best = divs
+      }
+    }
+    return step
+  }
+
+  if axis == none or axis.ticks == none { return () }
+  if axis.ticks.step == auto {
+    axis.ticks.step = find-max-n-ticks(axis, n: style.auto-tick-count)
+  }
+  if axis.ticks.minor-step == auto {
+    axis.ticks.minor-step = if axis.ticks.step != none {
+      axis.ticks.step / 5
+    } else {
+      none
+    }
+  }
+
+  let ticks = if axis.mode == "log" {
+    compute-logarithmic-ticks(axis, style, add-zero: add-zero)
+  } else {
+    compute-linear-ticks(axis, style, add-zero: add-zero)
+  }
+  ticks += fixed-ticks(axis)
+  return ticks
+}