curd

curd defines a 3D curve by number, as a polyline or as a cubic spline through control points.

Syntax

curd number lp3 x y z [ x y z ... ] ; [ operator ... ; ]
curd number csp3 option [ end_value ... ] x y z [ x y z ... ] ; [ operator ... ; ]

number: the curve’s number, a whole number of 1 or more. cur, curf, cure and curs refer to the curve by it.
lp3: a polyline through the points, in order.
csp3: a cubic spline through the points.
x y z: the coordinates of a control point. A curve needs at least two, and the count of numbers must be a multiple of three.
operator: an optional transformation, the operators of tr, ended by ;. James applies it to the control points.

A curd holds one type group, lp3 or csp3. Extra ; after the point list are ignored.

csp3 takes an option first. It is the word loop, which closes the spline into a smooth loop and takes no end value, or two digits. The first digit says how the first point is held and the second digit how the last is held:

Digit	Condition at that end	Values that follow the option
`0`	natural: second derivative zero	none
`1`	a derivative vector	three reals `dx dy dz`
`2`	matches the first end of another curve	a curve number and a magnitude
`3`	matches the last end of another curve	a curve number and a magnitude

The values of the first digit come before those of the second. A match takes the other curve’s unit tangent at the named end and scales it by the magnitude.

What it does

curd adds one curve to the table of 3D curves. A curve is geometry for the attach commands to use and moves nothing by itself. lp3 is exact geometry: straight segments. csp3 solves a cubic spline whose parameter runs by unit steps between control points, and every end condition is honoured.

When James applies it

When it is read, in any phase. curd is a definition, not a step of the hierarchy. A curve that csp3 matches must be defined before the curve that matches it.

Rules James adds

One type group per curd. A second group on the same command is refused with E0608, a recognised type that James does not support with E0603, and an unknown word with E0104.
A transformation word that follows the point list on the same line as the last ; is read as part of the curd. A line that starts with ; continues the curd, so a transformation word after that ; belongs to it too. Case 153-curd-stray-semicolon-trans shows both: its curve 3 ends one line with ; and starts the next with ; mx 1;, and the IR gives curve 3 the transformation row.
A word that starts a new line is read as the next command, whatever it is. A transformation word such as mx there is not a command, and James reports it as not recognized (E0105).
A loop needs at least three points.
A curve number below 1 is refused.

Diagnostics

E0601: a curve that csp3 matches is not defined.
E0602: fewer than two points.
E0603: a recognised curve type other than lp3 or csp3. An unknown word is E0104.
E0605: the count of coordinates is not a multiple of three.
E0606: the csp3 option is not recognised, or its end values are the wrong number.
E0608: a second type group.
E0104: the curve number is missing or below 1.

Example

The script tests/corpus/153-curd-stray-semicolon-trans/input.tg, which make test runs:

curd 1 lp3 0 0 0 1 1 1 2 2 2;;
curd 2 lp3 0 0 0 1 1 1 2 2 2; ; mx 1;
curd 3 lp3 0 0 0 1 1 1;
; mx 1;
block 1 2;1 2;1 2;0 1;0 1;0 1;
endpart

The three curves are polylines. Curve 1 ends in two semicolons. Curve 2 has a stray ;, then mx 1 on the same line, which the IR holds as a transformation row. Curve 3 has two points, and its mx 1 is on the next line after a ;. The IR holds three curves and two transformation rows, and the part is unaffected.