CadCraft™ v0.8.1
Use it now
Menu

Resources Numerical accuracy Calculation policy

User coordinate system set by command

Works out the origin and angle of the user coordinate system that UCS and the quarter-turn commands set, and what they print.

How the precision is kept

The origin is the picked point as stored and the angle is one atan2 toward a second point, or the current angle plus a typed angle or plus or minus π ÷ 2, in 64-bit. ucs.js setUcs then normalizes the angle to 0…2π. Objects keep their world coordinates; the system only changes how coordinates are typed and read out.

Open item. Use one tolerance for the X-axis point in the UCS command and in ucs.js threePoint, and keep the current angle when threePoint returns nothing.

Calculations under this policy

4 calculations in 1 source file. The code is read from the released app when this page loads. It is the calculation people run, not a copy kept for this page.

commands.js CadCraft 0.8.2 64-bit 4 calculations Reviewed

Tests bin/test-cadcraft.mjs

Origin and X axis from two points

64-bit

The coordinate system with its origin at a picked point and its X axis toward a second point.

origin = o; angle = atan2(pₓ − o) (ucs.js threePoint)

The origin is the picked point with no arithmetic. A second point more than 1e-12 drawing units (absolute) away is passed to ucs.js threePoint, which takes the angle by atan2 but returns nothing for a distance under 1e-9; a point between the two tolerances therefore sets the world system. With no second point the current angle is kept.

  • commands.js
  • lines 3471 to 3474
  • CadCraft 0.8.2
const o = { x: r.x, y: r.y };
c.preview((p) => [{ type: 'line', x1: o.x, y1: o.y, x2: p.x, y2: p.y }]);
const px = await c.point(t('cmd.ucs.xaxis'), { base: o, none: true });
setUcs(c.doc, px && dist(o, px) > 1e-12 ? threePoint(o, px) : { x: o.x, y: o.y, ang: cur ? cur.ang : 0 });

Rotation about Z

64-bit

The coordinate system turned by a typed angle about its own origin.

angle = current angle + a (a defaults to π ÷ 2)

One addition in radians; the typed angle was converted from degrees with × π ÷ 180. The origin is unchanged. ucs.js setUcs normalizes the sum to 0…2π.

  • commands.js
  • lines 3483 to 3485
  • CadCraft 0.8.2
if (key === 'Z') {
  const a = await c.angle(t('cmd.ucs.zangle'), { default: Math.PI / 2 });
  setUcs(c.doc, { x: cur ? cur.x : 0, y: cur ? cur.y : 0, ang: (cur ? cur.ang : 0) + (typeof a === 'number' ? a : Math.PI / 2) });

Quarter turn

64-bit

The coordinate system turned a quarter left or right, or set back to the world.

angle = current angle ± π ÷ 2

Adds or subtracts Math.PI ÷ 2 from the current angle; a sign of 0 sets the world system outright. The sum is not normalized here.

  • commands.js
  • lines 3530 to 3537
  • CadCraft 0.8.2
// View › More: turn the view a quarter (= UCS Z ∓90, then the view follows) or back to the world; their own names, so
// the aliases file can give them a key (ALIASEDIT: TL=TURNLEFT)
function quarterTurn(c, sign) {
  if (!c.doc.inModel) { c.print(t('cmd.ucs.sheet')); return; }
  const cur = c.doc.ucs;
  setUcs(c.doc, sign ? { x: cur ? cur.x : 0, y: cur ? cur.y : 0, ang: (cur ? cur.ang : 0) + sign * Math.PI / 2 } : null);
  afterUcs(c);
}

What UCS prints

64-bit

The origin and angle of the coordinate system as printed in the command history.

angle shown = (angle mod 2π) × 180 ÷ π, at most 4 decimals

The origin is written with the drawing's length format and the angle in degrees through fmt, which keeps at most 4 decimals. The stored system is not rounded.

  • commands.js
  • line 3458
  • CadCraft 0.8.2
const ucsLabel = (c, u) => (u ? t('cmd.ucs.is', { at: fmtLen(c, u.x) + ', ' + fmtLen(c, u.y), ang: fmt(deg(normAngle(u.ang))) }) : t('cmd.ucs.world'));

In detail

Method
Origin and X-axis point, rotation about Z by an angle, or a quarter turn; the angle is kept in radians.
Number types
64-bit numbers.
Tolerances
1e-12 drawing units, absolute, in this file: an X-axis point closer than this to the origin keeps the current angle. ucs.js threePoint returns no system below 1e-9.
Limits
The two tolerances differ: after a new origin, an X-axis point between 1e-12 and 1e-9 drawing units from it passes this file's test, gets no system from threePoint, and sets the world system.

Approach: 64-bit, direct

Every value is a 64-bit number from input to result. Formulas are closed form or a direct solve, and every comparison uses a stated tolerance.

Every policy that takes this approach