cubicsuperpath.py

#!/usr/bin/env python
"""
cubicsuperpath.py

Copyright (C) 2005 Aaron Spike, aaron@ekips.org

This program 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 2 of the License, or
(at your option) any later version.

This program 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 this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA

"""
import simplepath
from math import *


def matprod(mlist):
    prod = mlist[0]
    for m in mlist[1:]:
        a00 = prod[0][0] * m[0][0] + prod[0][1] * m[1][0]
        a01 = prod[0][0] * m[0][1] + prod[0][1] * m[1][1]
        a10 = prod[1][0] * m[0][0] + prod[1][1] * m[1][0]
        a11 = prod[1][0] * m[0][1] + prod[1][1] * m[1][1]
        prod = [[a00, a01], [a10, a11]]
    return prod


def rotmat(teta):
    return [[cos(teta), -sin(teta)], [sin(teta), cos(teta)]]


def applymat(mat, pt):
    x = mat[0][0] * pt[0] + mat[0][1] * pt[1]
    y = mat[1][0] * pt[0] + mat[1][1] * pt[1]
    pt[0] = x
    pt[1] = y


def norm(pt):
    return sqrt(pt[0] * pt[0] + pt[1] * pt[1])


def ArcToPath(p1, params):
    A = p1[:]
    rx, ry, teta, longflag, sweepflag, x2, y2 = params[:]
    teta = teta * pi / 180.0
    B = [x2, y2]
    if rx == 0 or ry == 0:
        return ([[A, A, A], [B, B, B]])
    mat = matprod((rotmat(teta), [[1 / rx, 0], [0, 1 / ry]], rotmat(-teta)))
    applymat(mat, A)
    applymat(mat, B)
    k = [-(B[1] - A[1]), B[0] - A[0]]
    d = k[0] * k[0] + k[1] * k[1]
    k[0] /= sqrt(d)
    k[1] /= sqrt(d)
    d = sqrt(max(0, 1 - d / 4))
    if longflag == sweepflag:
        d *= -1
    O = [(B[0] + A[0]) / 2 + d * k[0], (B[1] + A[1]) / 2 + d * k[1]]
    OA = [A[0] - O[0], A[1] - O[1]]
    OB = [B[0] - O[0], B[1] - O[1]]
    start = acos(OA[0] / norm(OA))
    if OA[1] < 0:
        start *= -1
    end = acos(OB[0] / norm(OB))
    if OB[1] < 0:
        end *= -1

    if sweepflag and start > end:
        end += 2 * pi
    if (not sweepflag) and start < end:
        end -= 2 * pi

    NbSectors = int(abs(start - end) * 2 / pi) + 1
    dTeta = (end - start) / NbSectors
    # v=dTeta*2/pi*0.552
    # v=dTeta*2/pi*4*(sqrt(2)-1)/3
    v = 4 * tan(dTeta / 4) / 3
    # if not sweepflag:
    #    v*=-1
    p = []
    for i in range(0, NbSectors + 1, 1):
        angle = start + i * dTeta
        v1 = [O[0] + cos(angle) - (-v) * sin(angle), O[1] + sin(angle) + (-v) * cos(angle)]
        pt = [O[0] + cos(angle), O[1] + sin(angle)]
        v2 = [O[0] + cos(angle) - v * sin(angle), O[1] + sin(angle) + v * cos(angle)]
        p.append([v1, pt, v2])
    p[0][0] = p[0][1][:]
    p[-1][2] = p[-1][1][:]

    mat = matprod((rotmat(teta), [[rx, 0], [0, ry]], rotmat(-teta)))
    for pts in p:
        applymat(mat, pts[0])
        applymat(mat, pts[1])
        applymat(mat, pts[2])
    return (p)


def CubicSuperPath(simplepath):
    csp = []
    subpath = -1
    subpathstart = []
    last = []
    lastctrl = []
    for s in simplepath:
        cmd, params = s
        if cmd == 'M':
            if last:
                csp[subpath].append([lastctrl[:], last[:], last[:]])
            subpath += 1
            csp.append([])
            subpathstart = params[:]
            last = params[:]
            lastctrl = params[:]
        elif cmd == 'L':
            csp[subpath].append([lastctrl[:], last[:], last[:]])
            last = params[:]
            lastctrl = params[:]
        elif cmd == 'C':
            csp[subpath].append([lastctrl[:], last[:], params[:2]])
            last = params[-2:]
            lastctrl = params[2:4]
        elif cmd == 'Q':
            q0 = last[:]
            q1 = params[0:2]
            q2 = params[2:4]
            x0 = q0[0]
            x1 = 1. / 3 * q0[0] + 2. / 3 * q1[0]
            x2 = 2. / 3 * q1[0] + 1. / 3 * q2[0]
            x3 = q2[0]
            y0 = q0[1]
            y1 = 1. / 3 * q0[1] + 2. / 3 * q1[1]
            y2 = 2. / 3 * q1[1] + 1. / 3 * q2[1]
            y3 = q2[1]
            csp[subpath].append([lastctrl[:], [x0, y0], [x1, y1]])
            last = [x3, y3]
            lastctrl = [x2, y2]
        elif cmd == 'A':
            arcp = ArcToPath(last[:], params[:])
            arcp[0][0] = lastctrl[:]
            last = arcp[-1][1]
            lastctrl = arcp[-1][0]
            csp[subpath] += arcp[:-1]
        elif cmd == 'Z':
            csp[subpath].append([lastctrl[:], last[:], last[:]])
            last = subpathstart[:]
            lastctrl = subpathstart[:]
    # append final superpoint
    csp[subpath].append([lastctrl[:], last[:], last[:]])
    return csp


def unCubicSuperPath(csp):
    a = []
    for subpath in csp:
        if subpath:
            a.append(['M', subpath[0][1][:]])
            for i in range(1, len(subpath)):
                a.append(['C', subpath[i - 1][2][:] + subpath[i][0][:] + subpath[i][1][:]])
    return a


def parsePath(d):
    return CubicSuperPath(simplepath.parsePath(d))


def formatPath(p):
    return simplepath.formatPath(unCubicSuperPath(p))

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