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bl_info = {
    "name": "Simplify Curves",
    "author": "testscreenings",
    "version": (1, 0, 1),
    "blender": (2, 75, 0),
    "location": "Search > Simplify Curves",
    "description": "Simplifies 3D Curve objects and animation F-Curves",
    "warning": "",
    "wiki_url": "http://wiki.blender.org/index.php/Extensions:2.6/Py/"
                "Scripts/Curve/Curve_Simplify",
    "category": "Add Curve",
}

"""
This script simplifies Curve objects and animation F-Curves.
"""

####################################################
import bpy
from bpy.props import *
import mathutils
import math

from bpy.types import Menu
  

    ## Check for curve

##############################
#### simplipoly algorithm ####
##############################
# get SplineVertIndices to keep
def simplypoly(splineVerts, options):
    # main vars
    newVerts = [] # list of vertindices to keep
    points = splineVerts # list of 3dVectors
    pointCurva = [] # table with curvatures
    curvatures = [] # averaged curvatures per vert
    for p in points:
        pointCurva.append([])
    order = options[3] # order of sliding beziercurves
    k_thresh = options[2] # curvature threshold
    dis_error = options[6] # additional distance error

    # get curvatures per vert
    for i, point in enumerate(points[:-(order-1)]):
        BVerts = points[i:i+order]
        for b, BVert in enumerate(BVerts[1:-1]):
            deriv1 = getDerivative(BVerts, 1/(order-1), order-1)
            deriv2 = getDerivative(BVerts, 1/(order-1), order-2)
            curva = getCurvature(deriv1, deriv2)
            pointCurva[i+b+1].append(curva)

    # average the curvatures
    for i in range(len(points)):
        avgCurva = sum(pointCurva[i]) / (order-1)
        curvatures.append(avgCurva)

    # get distancevalues per vert - same as Ramer-Douglas-Peucker
    # but for every vert
    distances = [0.0] #first vert is always kept
    for i, point in enumerate(points[1:-1]):
        dist = altitude(points[i], points[i+2], points[i+1])
        distances.append(dist)
    distances.append(0.0) # last vert is always kept

    # generate list of vertindices to keep
    # tested against averaged curvatures and distances of neighbour verts
    newVerts.append(0) # first vert is always kept
    for i, curv in enumerate(curvatures):
        if (curv >= k_thresh*0.01
        or distances[i] >= dis_error*0.1):
            newVerts.append(i)
    newVerts.append(len(curvatures)-1) # last vert is always kept

    return newVerts

# get binomial coefficient
def binom(n, m):
    b = [0] * (n+1)
    b[0] = 1
    for i in range(1, n+1):
        b[i] = 1
        j = i-1
        while j > 0:
            b[j] += b[j-1]
            j-= 1
    return b[m]

# get nth derivative of order(len(verts)) bezier curve
def getDerivative(verts, t, nth):
    order = len(verts) - 1 - nth
    QVerts = []

    if nth:
        for i in range(nth):
            if QVerts:
                verts = QVerts
            derivVerts = []
            for i in range(len(verts)-1):
                derivVerts.append(verts[i+1] - verts[i])
            QVerts = derivVerts
    else:
        QVerts = verts

    if len(verts[0]) == 3:
        point = mathutils.Vector((0, 0, 0))
    if len(verts[0]) == 2:
        point = mathutils.Vector((0, 0))

    for i, vert in enumerate(QVerts):
        point += binom(order, i) * math.pow(t, i) * math.pow(1-t, order-i) * vert
    deriv = point

    return deriv

# get curvature from first, second derivative
def getCurvature(deriv1, deriv2):
    if deriv1.length == 0: # in case of points in straight line
        curvature = 0
        return curvature
    curvature = (deriv1.cross(deriv2)).length / math.pow(deriv1.length, 3)
    return curvature

#########################################
#### Ramer-Douglas-Peucker algorithm ####
#########################################
# get altitude of vert
def altitude(point1, point2, pointn):
    edge1 = point2 - point1
    edge2 = pointn - point1
    if edge2.length == 0:
        altitude = 0
        return altitude
    if edge1.length == 0:
        altitude = edge2.length
        return altitude
    alpha = edge1.angle(edge2)
    altitude = math.sin(alpha) * edge2.length
    return altitude

# iterate through verts
def iterate(points, newVerts, error):
    new = []
    for newIndex in range(len(newVerts)-1):
        bigVert = 0
        alti_store = 0
        for i, point in enumerate(points[newVerts[newIndex]+1:newVerts[newIndex+1]]):
            alti = altitude(points[newVerts[newIndex]], points[newVerts[newIndex+1]], point)
            if alti > alti_store:
                alti_store = alti
                if alti_store >= error:
                    bigVert = i+1+newVerts[newIndex]
        if bigVert:
            new.append(bigVert)
    if new == []:
        return False
    return new

#### get SplineVertIndices to keep
def simplify_RDP(splineVerts, options):
    #main vars
    error = options[4]

    # set first and last vert
    newVerts = [0, len(splineVerts)-1]

    # iterate through the points
    new = 1
    while new != False:
        new = iterate(splineVerts, newVerts, error)
        if new:
            newVerts += new
            newVerts.sort()
    return newVerts

##########################
#### CURVE GENERATION ####
##########################
# set bezierhandles to auto
def setBezierHandles(newCurve):

    #bpy.ops.object.mode_set(mode='EDIT', toggle=True)
    #bpy.ops.curve.select_all(action='SELECT')
    #bpy.ops.curve.handle_type_set(type='AUTOMATIC')
    #bpy.ops.object.mode_set(mode='OBJECT', toggle=True)

    # Faster:
    for spline in newCurve.data.splines:
        for p in spline.bezier_points:
            p.handle_left_type = 'AUTO'
            p.handle_right_type = 'AUTO'

# get array of new coords for new spline from vertindices
def vertsToPoints(newVerts, splineVerts, splineType):
    # main vars
    newPoints = []

    # array for BEZIER spline output
    if splineType == 'BEZIER':
        for v in newVerts:
            newPoints += splineVerts[v].to_tuple()

    # array for nonBEZIER output
    else:
        for v in newVerts:
            newPoints += (splineVerts[v].to_tuple())
            if splineType == 'NURBS':
                newPoints.append(1) #for nurbs w=1
            else: #for poly w=0
                newPoints.append(0)
    return newPoints

#########################
#### MAIN OPERATIONS ####
#########################

def main(context, obj, options):
    #print("\n_______START_______")
    # main vars
    mode = options[0]
    output = options[1]
    degreeOut = options[5]
    keepShort = options[7]
    bpy.ops.object.select_all(action='DESELECT')
    scene = context.scene
    splines = obj.data.splines.values()

    # create curvedatablock
    curve = bpy.data.curves.new("Simple_"+obj.name, type = 'CURVE')

    # go through splines
    for spline_i, spline in enumerate(splines):
        # test if spline is a long enough
        if len(spline.points) >= 7 or keepShort:
            #check what type of spline to create
            if output == 'INPUT':
                splineType = spline.type
            else:
                splineType = output

            # get vec3 list to simplify
            if spline.type == 'BEZIER': # get bezierverts
                splineVerts = [splineVert.co.copy()
                                for splineVert in spline.bezier_points.values()]

            else: # verts from all other types of curves
                splineVerts = [splineVert.co.to_3d()
                                for splineVert in spline.points.values()]

            # simplify spline according to mode
            if mode == 'DISTANCE':
                newVerts = simplify_RDP(splineVerts, options)

            if mode == 'CURVATURE':
                newVerts = simplypoly(splineVerts, options)

            # convert indices into vectors3D
            newPoints = vertsToPoints(newVerts, splineVerts, splineType)

            # create new spline
            newSpline = curve.splines.new(type = splineType)

            # put newPoints into spline according to type
            if splineType == 'BEZIER':
                newSpline.bezier_points.add(int(len(newPoints)*0.33))
                newSpline.bezier_points.foreach_set('co', newPoints)
            else:
                newSpline.points.add(int(len(newPoints)*0.25 - 1))
                newSpline.points.foreach_set('co', newPoints)

            # set degree of outputNurbsCurve
            if output == 'NURBS':
                newSpline.order_u = degreeOut

            # splineoptions
            newSpline.use_endpoint_u = spline.use_endpoint_u

    # create ne object and put into scene
    newCurve = bpy.data.objects.new("Simple_"+obj.name, curve)
    scene.objects.link(newCurve)
    newCurve.select = True
    scene.objects.active = newCurve
    newCurve.matrix_world = obj.matrix_world

    # set bezierhandles to auto
    setBezierHandles(newCurve)

    #print("________END________\n")
    return

##################
## get preoperator fcurves
def getFcurveData(obj):
    fcurves = []
    for fc in obj.animation_data.action.fcurves:
        if fc.select:
            fcVerts = [vcVert.co.to_3d()
                        for vcVert in fc.keyframe_points.values()]
            fcurves.append(fcVerts)
    return fcurves

def selectedfcurves(obj):
    fcurves_sel = []
    for i, fc in enumerate(obj.animation_data.action.fcurves):
        if fc.select:
            fcurves_sel.append(fc)
    return fcurves_sel

###########################################################
## fCurves Main
def fcurves_simplify(context, obj, options, fcurves):
    # main vars
    mode = options[0]

    #get indices of selected fcurves
    fcurve_sel = selectedfcurves(obj)

    # go through fcurves
    for fcurve_i, fcurve in enumerate(fcurves):
        # test if fcurve is long enough
        if len(fcurve) >= 7:

            # simplify spline according to mode
            if mode == 'DISTANCE':
                newVerts = simplify_RDP(fcurve, options)

            if mode == 'CURVATURE':
                newVerts = simplypoly(fcurve, options)

            # convert indices into vectors3D
            newPoints = []

            #this is different from the main() function for normal curves, different api...
            for v in newVerts:
                newPoints.append(fcurve[v])

            #remove all points from curve first
            for i in range(len(fcurve)-1,0,-1):
                fcurve_sel[fcurve_i].keyframe_points.remove(fcurve_sel[fcurve_i].keyframe_points[i])
            # put newPoints into fcurve
            for v in newPoints:
                fcurve_sel[fcurve_i].keyframe_points.insert(frame=v[0],value=v[1])
            #fcurve.points.foreach_set('co', newPoints)
    return

### MENU ###

class GRAPH_OT_simplifyf(bpy.types.Menu):
    bl_space_type = "GRAPH_EDITOR"
    bl_label = "Simplify F Curves"

    def draw(self, context):
        layout = self.layout

def menu_func(self, context):
 	self.layout.operator(GRAPH_OT_simplify.bl_idname)

class CurveMenu(Menu):
    bl_space_type = "3D_VIEW"
    bl_label = "Simplify Curves"

    def draw(self, context):
        layout = self.layout

def menu(self, context):
    self.layout.operator("curve.simplify", text="Curve Simplify", icon="CURVE_DATA")

#################################################
#### ANIMATION CURVES OPERATOR ##################
#################################################
class GRAPH_OT_simplify(bpy.types.Operator):
    """"""
    bl_idname = "graph.simplify"
    bl_label = "Simplifiy F-Curves"
    bl_description = "Simplify selected Curves"
    bl_options = {'REGISTER', 'UNDO'}

    ## Properties
    opModes = [
            ('DISTANCE', 'Distance', 'Distance-based simplification (Poly)'),
            ('CURVATURE', 'Curvature', 'Curvature-based simplification (RDP)')]
    mode = EnumProperty(name="Mode",
                            description="Choose algorithm to use",
                            items=opModes)
    k_thresh = FloatProperty(name="k",
                            min=0, soft_min=0,
                            default=0, precision=3,
                            description="Threshold")
    pointsNr = IntProperty(name="n",
                            min=5, soft_min=5,
                            max=16, soft_max=9,
                            default=5,
                            description="Degree of curve to get averaged curvatures")
    error = FloatProperty(name="Error",
                            description="Maximum error to allow - distance",
                            min=0.0, soft_min=0.0,
                            default=0, precision=3)
    degreeOut = IntProperty(name="Degree",
                            min=3, soft_min=3,
                            max=7, soft_max=7,
                            default=5,
                            description="Degree of new curve")
    dis_error = FloatProperty(name="Distance error",
                            description="Maximum error in Blender Units to allow - distance",
                            min=0, soft_min=0,
                            default=0.0, precision=3)
    fcurves = []

    '''  Remove curvature mode as long as it isn't significantly improved

    def draw(self, context):
        layout = self.layout
        col = layout.column()
        col.label('Mode:')
        col.prop(self, 'mode', expand=True)
        if self.mode == 'DISTANCE':
            box = layout.box()
            box.label(self.mode, icon='ARROW_LEFTRIGHT')
            box.prop(self, 'error', expand=True)
        if self.mode == 'CURVATURE':
            box = layout.box()
            box.label('Degree', icon='SMOOTHCURVE')
            box.prop(self, 'pointsNr', expand=True)
            box.label('Threshold', icon='PARTICLE_PATH')
            box.prop(self, 'k_thresh', expand=True)
            box.label('Distance', icon='ARROW_LEFTRIGHT')
            box.prop(self, 'dis_error', expand=True)
        col = layout.column()
    '''

    def draw(self, context):
        layout = self.layout
        col = layout.column()
        col.label(text = "Simplify F-Curves")
        col.prop(self, 'error', expand=True)

    ## Check for animdata
    @classmethod
    def poll(cls, context):
        obj = context.active_object
        fcurves = False
        if obj:
            animdata = obj.animation_data
            if animdata:
                act = animdata.action
                if act:
                    fcurves = act.fcurves
        return (obj and fcurves)

    ## execute
    def execute(self, context):
        #print("------START------")

        options = [
                self.mode,       #0
                self.mode,       #1
                self.k_thresh,   #2
                self.pointsNr,   #3
                self.error,      #4
                self.degreeOut,  #6
                self.dis_error]  #7

        obj = context.active_object

        if not self.fcurves:
            self.fcurves = getFcurveData(obj)

        fcurves_simplify(context, obj, options, self.fcurves)

        #print("-------END-------")
        return {'FINISHED'}

###########################
##### Curves OPERATOR #####
###########################
class CURVE_OT_simplify(bpy.types.Operator):
    """"""
    bl_idname = "curve.simplify"
    bl_label = "Simplifiy Curves"
    bl_description = "Simplify Curves"
    bl_options = {'REGISTER', 'UNDO'}

    ## Properties
    opModes = [
            ('DISTANCE', 'Distance', 'Distance-based simplification (Poly)'),
            ('CURVATURE', 'Curvature', 'Curvature-based simplification (RDP)')]
    mode = EnumProperty(name="Mode",
                            description="Choose algorithm to use",
                            items=opModes)
    SplineTypes = [
                ('INPUT', 'Input', 'Same type as input spline'),
                ('NURBS', 'Nurbs', 'NURBS'),
                ('BEZIER', 'Bezier', 'BEZIER'),
                ('POLY', 'Poly', 'POLY')]
    output = EnumProperty(name="Output splines",
                            description="Type of splines to output",
                            items=SplineTypes)
    k_thresh = FloatProperty(name="k",
                            min=0, soft_min=0,
                            default=0, precision=3,
                            description="Threshold")
    pointsNr = IntProperty(name="n",
                            min=5, soft_min=5,
                            max=9, soft_max=9,
                            default=5,
                            description="Degree of curve to get averaged curvatures")
    error = FloatProperty(name="Error in Blender Units",
                            description="Maximum error in Blender Units to allow - distance",
                            min=0, soft_min=0,
                            default=0.0, precision=3)
    degreeOut = IntProperty(name="Degree",
                            min=3, soft_min=3,
                            max=7, soft_max=7,
                            default=5,
                            description="Degree of new curve")
    dis_error = FloatProperty(name="Distance error",
                            description="Maximum error in Blender Units to allow - distance",
                            min=0, soft_min=0,
                            default=0.0)
    keepShort = BoolProperty(name="Keep short splines",
                            description="Keep short splines (less then 7 points)",
                            default=True)

    '''  Remove curvature mode as long as it isn't significantly improved

    def draw(self, context):
        layout = self.layout
        col = layout.column()
        col.label('Mode:')
        col.prop(self, 'mode', expand=True)
        if self.mode == 'DISTANCE':
            box = layout.box()
            box.label(self.mode, icon='ARROW_LEFTRIGHT')
            box.prop(self, 'error', expand=True)
        if self.mode == 'CURVATURE':
            box = layout.box()
            box.label('Degree', icon='SMOOTHCURVE')
            box.prop(self, 'pointsNr', expand=True)
            box.label('Threshold', icon='PARTICLE_PATH')
            box.prop(self, 'k_thresh', expand=True)
            box.label('Distance', icon='ARROW_LEFTRIGHT')
            box.prop(self, 'dis_error', expand=True)
        col = layout.column()
        col.separator()
        col.prop(self, 'output', text='Output', icon='OUTLINER_OB_CURVE')
        if self.output == 'NURBS':
            col.prop(self, 'degreeOut', expand=True)
        col.prop(self, 'keepShort', expand=True)
    '''

    def draw(self, context):
        layout = self.layout
        col = layout.column()
        col.prop(self, 'error', expand=True)
        col.prop(self, 'output', text='Output', icon='OUTLINER_OB_CURVE')
        if self.output == 'NURBS':
            col.prop(self, 'degreeOut', expand=True)
        col.prop(self, 'keepShort', expand=True)


    @classmethod
    def poll(cls, context):
        obj = context.active_object
        return (obj and obj.type == 'CURVE')

    ## execute
    def execute(self, context):
        #print("------START------")

        options = [
                self.mode,       #0
                self.output,     #1
                self.k_thresh,   #2
                self.pointsNr,   #3
                self.error,      #4
                self.degreeOut,  #5
                self.dis_error,  #6
                self.keepShort]  #7


        bpy.context.user_preferences.edit.use_global_undo = False

        bpy.ops.object.mode_set(mode='OBJECT', toggle=True)
        obj = context.active_object

        main(context, obj, options)

        bpy.context.user_preferences.edit.use_global_undo = True

        #print("-------END-------")
        return {'FINISHED'}

#################################################
#### REGISTER ###################################
#################################################
def register():
    bpy.utils.register_module(__name__)

    bpy.types.GRAPH_MT_channel.append(menu_func)
    bpy.types.DOPESHEET_MT_channel.append(menu_func)
    bpy.types.INFO_MT_curve_add.append(menu)

def unregister():

    bpy.types.GRAPH_MT_channel.remove(menu_func)
    bpy.types.DOPESHEET_MT_channel.remove(menu_func)
    bpy.types.INFO_MT_curve_add.remove(menu)

    bpy.utils.unregister_module(__name__)

if __name__ == "__main__":
    register()

