Gojo · A justified local space

Affine basis construction

Connect two spans, establish their coordinate roles, and keep the calibration when the basis crystallizes. A Bézier can then use that space—even when some of its points are only partly known.

Available structure
Read in the selected basis
Still open

Turning or reflecting the view changes only the picture. Viewing from the back mirrors left and right while keeping the viewer’s top and bottom. The opposite convention changes a coordinate read through its retained calibration; it does not move the represented point.

Look at the actual syntax

Excerpts from the executable fixture. The selected reader crystallizes the foundation and binds its result to ?basis. The same six interpolation requests then consume that basis.

let $origin = point(carrier(),0);
let $line = crystal(orthogonal($origin -> $origin));
let $a = point($line,0);
let $b = point($line,6);
let $edge = $a -> $b;
let $outlet = orthogonal($edge);
let $cross = crystal(orthogonal($a -> $a));
let $cross_start = point($cross,0);
let $d = point($cross,4);
let $cross_span = $cross_start -> $d;
let $selection = $outlet -> $cross_span;
let $common_origin = $a -> $cross_start;
let $foundation = group($edge, $selection, $common_origin);

root group(?basis, group(at($line,3), ?unobserved_cross));

let $grade = group(?sample, $domain, $domain, ?basis);
let $ab = ports(?start, ?control_a, $grade) -> ?q0;
let $bc = ports(?control_a, ?control_b, $grade) -> ?q1;
let $cd = ports(?control_b, ?end, $grade) -> ?q2;
let $abc = ports(?q0, ?q1, $grade) -> ?r0;
let $bcd = ports(?q1, ?q2, $grade) -> ?r1;
let $result = ports(?r0, ?r1, $grade) -> ?curve_point;

Full authored fixture

What has this experiment established?

The kernel checks the span connections, native line provenance and calibrations, captures the basis, and evaluates each interpolation. The numeric traces on this page are checked against those readers. The browser draws an illustration of those results.

The affine product interpretation is selected as a local construction rule. This does not discover physical independence, measure a right angle, or infer a metric from two carriers. The two units are drawn at equal screen lengths for clarity; that does not make their physical lengths equal. Partial signals can contain both first-axis and orthogonal participation; automatic discovery of that decomposition is separate work.

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