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PLaSM.js curves

curves

Bezier

BEZIER(sel)(controlpoints)

Transfinite mapping function of genric degree Bezier curve.

I/O

⇒ Function selector: domain coordinate selector function.

⇒ Array v: point of the domain.

⇐ Number: the selected coordinate.

⇐ Function: an anonymous function.

⇒ Array controlpoints: an array of points and curve mapping functions describing curve control points.

⇐ Function: an anonymous mapping function.

Example

var domain = INTERVALS(1)(32);
var controls = [[-0,0],[1,0],[1,1],[2,1],[3,1]];
var mapping = BEZIER(S0)(controls);
var curve = MAP(mapping)(domain);
DRAW(curve);
var domain = PROD1x1([INTERVALS(1)(16),INTERVALS(1)(16)]);
var c0 = BEZIER(S0)([[0,0,0],[10,0,0]]);
var c1 = BEZIER(S0)([[0,2,0],[8,3,0],[9,2,0]]);
var c2 = BEZIER(S0)([[0,4,1],[7,5,-1],[8,5,1],[12,4,0]]);
var c3 = BEZIER(S0)([[0,6,0],[9,6,3],[10,6,-1]]);
var surface = MAP(BEZIER(S1)([c0,c1,c2,c3]))(domain);
DRAW(surface);

CUBIC_HERMITE(selector)(controlpoints)

Transfinite mapping function of cubic Hermite curve.

I/O

⇒ Function selector: domain coordinate selector function.

⇒ Array v: point of the domain.

⇐ Number: the selected coordinate.

⇐ Function: an anonymous function.

⇒ Array controlpoints: an array of points and curve mapping functions describing curve control points.

⇐ Function: an anonymous mapping function.

Example

var domain = INTERVALS(1)(20);
var controls = [[1,0],[1,1],[ -1, 1],[ 1,0]];
var mapping = CUBIC_HERMITE(S0)(controls);
var curve = MAP(mapping)(domain);
DRAW(curve);
var domain = PROD1x1([INTERVALS(1)(14),INTERVALS(1)(14)]);
var c1 = CUBIC_HERMITE(S0)([[1,0,0],[0,1,0],[0,3,0],[-3,0,0]]);
var c2 = CUBIC_HERMITE(S0)([[0.5,0,0],[0,0.5,0],[0,1,0],[-1,0,0]]);
var mapping = CUBIC_HERMITE(S1)([c1,c2,[1,1,1],[-1,-1,-1]]);
var surface = MAP(sur3)(domain);
DRAW(surface);

NUBSLINE(degree)(knots)(controls)

Non-uniform B-Spline.

I/O

⇒ Number degree: spline degree.

⇐ Function: an anonymous function.

⇒ Array knots: Array of integer describing spline's knots.

⇐ Function: an anonymous function.

⇒ Array controls: Array of integer describing spline's control points.

⇐ plasm.Model: non uniform spline.

Example

var controls = [[0,0],[-1,2],[1,4],[2,3],[1,1],[1,2],[2.5,1],[2.5,3],[4,4],[5,0]];
var knots = [0,0,0,0,1,2,3,4,5,6,7,7,7,7];
var nubspline = NUBSPLINE(3)(knots)(controls);
DRAW(nubspline);

NUBS(sel)(degree)(knots)(controls)

Transfinite Non-uniform B-Spline.

I/O

⇒ Function sel: selctor function.

⇐ Function: an anonymous function.

⇒ Number degree: spline degree.

⇐ Function: an anonymous function.

⇒ Array knots: Array of integer describing spline's knots.

⇐ Function: an anonymous function.

⇒ Array controls: Array of integer describing spline's control points.

⇐ plasm.Model: non uniform spline.

Example

var domain = INTERVALS(1)(20);
var controls = [[0,0],[-1,2],[1,4],[2,3],[1,1],[1,2],[2.5,1],[2.5,3],[4,4],[5,0]];
var nubs = NUBS(S0)(3)([0,0,0,0,1,2,3,4,5,6,7,7,7,7])(controls);
var model = MAP(nubs)(domain);
DRAW(model);
var domain = DOMAIN([[0,1],[0,1]])([30,30]);
var b0 = BEZIER(S0)([[0,0,0],[5,-10,0],[10,0,0]]);
var b1 = BEZIER(S0)([[0,2,0],[8,3,0],[9,2,0]]);
var b2 = BEZIER(S0)([[0,4,1],[7,5,-1],[8,5,1],[12,4,0]]);
var b3 = BEZIER(S0)([[0,6,0],[9,6,3],[10,6,-1]]);
var controls = [b0,b1,b2,b3];
var nubs = NUBS(S1)(3)([0,0,0,0,7,7,7,7])(controls);
var model = MAP(nubs)(domain);
DRAW(model);

NURBSLINE(degree)(knots)(controls)

Non-uniform Rational B-Spline.

I/O

⇒ Number degree: spline degree.

⇐ Function: an anonymous function.

⇒ Array knots: Array of integer describing spline's knots.

⇐ Function: an anonymous function.

⇒ Array controls: Array of integer describing spline's control points.

⇐ plasm.Model: non uniform rational spline.

Example

var p = SQRT(2)/2.0;
var controls = [[-1,0,1], [-p,p,p], [0,1,1], [p,p,p], [1,0,1], [p,-p,p], [0,-1,1], [-p,-p,p], [-1,0,1]];
var knots = [0,0,0,1,1,2,2,3,3,4,4,4];
var nurbs = NURBSPLINE(2)(knots)(controls);
DRAW(nurbs);

SPLINE(curve)(controlpoints)

Create spline curve.

I/O

⇒ Function curve: spline curve generator function, such as the result of application of CUBIC_UBSPLINE or CUBIC_CARDINAL to a domain.

⇐ Function: an anonymous function.

⇒ Array controlpoints: an array of points and curve mapping functions describing curve control points.

⇐ plasm.Struct: the spline.

Example

var domain = INTERVALS(1)(20);
var controlpoints = [[-3,6],[-4,2],[-3,-1],[-1,1],[1.5,1.5],[3,4],[5,5],[7,2],[6,-2],[2,-3]];
var splineCardinal = COLOR([1,0,0])(SPLINE(CUBIC_CARDINAL(domain))(controlpoints));
var splineCubic = COLOR([0,1,0])(SPLINE(CUBIC_UBSPLINE(domain))(controlpoints));
var points = SIMPLICIAL_COMPLEX(controlpoints)([[0],[1],[2],[3],[4],[5],[6],[7],[8],[9]]);
var out = STRUCT([splineCardinal,splineCubic,points]);
DRAW(out);

CUBIC_CARDINAL(domain)

Tranfinite Cubic cardinal splines curve generator function on domain.

I/O

⇒ plasm.Model domain: domain of the generator function.

⇐ Function: an anonymous function.

⇒ Array controlpoints: an array of points and curve mapping functions describing curve control points.

⇐ plasm.Model: a spline segment.

Example

var domain = INTERVALS(1)(20);
var controls = [[-3,6],[-4,2],[-3,-1],[-1,1],[1.5,1.5],[3,4],[5,5],[7,2],[6,-2],[2,-3]];
var spline = SPLINE(CUBIC_CARDINAL(domain))(controlpoints);
DRAW(spline);

CUBIC_UBSPLINE(domain)

Tranfinite cubic uniform B-splines curve generator function on domain.

I/O

⇒ plasm.Model domain: domain of the generator function.

⇐ Function: an anonymous function.

⇒ Array controlpoints: an array of points and curve mapping functions describing curve control points.

⇐ plasm.Model: a spline segment.

Example

var domain = INTERVALS(1)(20);
var controls = [[-3,6],[-4,2],[-3,-1],[-1,1],[1.5,1.5],[3,4],[5,5],[7,2],[6,-2],[2,-3]];
var spline = SPLINE(CUBIC_UBSPLINE(domain))(controlpoints);
DRAW(spline);