/** This file is part of Shapes.
 **
 ** Shapes is free software: you can redistribute it and/or modify
 ** it under the terms of the GNU General Public License as published by
 ** the Free Software Foundation, either version 3 of the License, or
 ** any later version.
 **
 ** Shapes is distributed in the hope that it will be useful,
 ** but WITHOUT ANY WARRANTY; without even the implied warranty of
 ** MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 ** GNU General Public License for more details.
 **
 ** You should have received a copy of the GNU General Public License
 ** along with Shapes.  If not, see <http://www.gnu.org/licenses/>.
 **
 ** Copyright 2008, 2010, 2013, 2014 Henrik Tidefelt
 **/

##needs ..Shapes..Geometry / linkpaths
##needs ..Shapes..Data / seq-support

##lookin ..Shapes
##lookin ..Shapes..Geometry

/** The mergepaths function turned out difficult to implement since the subpath function
 ** does not return the control point at the free end of the cut (this is often a desirable
 ** behavior).  Instead the function meetpaths was added to the kernel.
**/
|**pathpoint: \ p t →
|**  (+[reversespeed p t]*[reversedirection p t])<
|**  [point p t]
|**  >(+[speed p t]*[direction p t])
|**
|**mergepaths: \ p1 p2 →
|**  [if [Geometry..duration p1]>1
|**      { t:([Geometry..duration p1]-1)  [subpath p1 0 t]>(+[speed p1 t]*[direction p1 t]) }
|**      [pathpoint p1 0]]
|**  --
|**  (+[reversespeed p1 ∞]*[reversedirection p1 ∞])<
|**  ( 0.5 * ( [point p1 ∞] + [point p2 0] ) )
|**  >(+[speed p2 0]*[direction p2 0])
|**  --
|**  [if [Geometry..duration p2]>1
|**      (+[reversespeed p 1]*[reversedirection p 1])<[subpath p2 1 ∞]
|**      [pathpoint p2 ∞]]

Geometry..@defaultunit: 1%c
|
{
  pth1: (~1cm,0cm)--(^)<(0cm,0cm)>(1cm,1cm)--(2cm,3cm)<(4cm,4cm)>(^)
  pth2: (^)<(5cm,4cm)>(5cm,5cm)--(1cm^180°)<(7cm,3cm)>(^)--(7cm,2cm)

  Traits..@stroking:[Traits..gray 0.7]
  |
  {
    IO..•page << [Graphics..stroke pth1]
    IO..•page << [Graphics..stroke pth2]
  }

  IO..•page << [Graphics..stroke [Geometry..meetpaths pth1 pth2]]
}

Geometry..@defaultunit: 1%c
|
{
  pth1: (0cm,~3cm)>(2cm^70°)--(5cm,5cm)
  pth2: (3cm,~2cm)>(2cm^140°)--(0cm,4cm)

  Traits..@stroking:[Traits..gray 0.7]
  |
  {
    IO..•page << [Graphics..stroke pth1] << [Graphics..stroke pth2]
  }

  IO..•page << [Graphics..stroke [Geometry..linkpaths pth1 pth2]]
}

{
  subpath: \ pth t1 t2 → [pth t1]--[pth t2]
  seg: \ a → [shift (5cm,0)]*[rotate a]*[shift (0,~1.2cm)] [] [Geometry..reverse [subpath [Geometry..circle 1cm] 0 1.5]]
  c1: [seg 0°]
  c2: [seg 90°]
  c3: [seg 180°]
  c4: [seg 270°]
  IO..•page << [Graphics..stroke c1]
  pths: [Data..list c1 c2 c3 c4]

  IO..•page << [pths.foldl
             \ p e → p & [Graphics..stroke e]
             Graphics..null]

  scaleAroundCenter: \ factor pth → { c: [Geometry..mean pth]  [shift c]*[scale factor]*[shift ~c] [] pth }
  IO..•page << Traits..@stroking: Traits..RGB..RED | [Graphics..stroke [scaleAroundCenter 1.3 ...][] [Geometry..buildchain pths]--cycle]
}