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Commit Message

Merge 28adcc8e5 into ccf4f61e9

Pull Request Pull Request #84: Enh/meshplot

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/pymech/meshplot.py

import wx
from wx import glcanvas
import OpenGL.GL as gl
import numpy as np
from math import sqrt, atan2, asin, cos, sin


class MeshFrame(wx.Frame):
    """
    A frame to display meshes
    """

    def __init__(
        self,
        mesh,
        parent,
        id,
        title,
        pos=wx.DefaultPosition,
        size=wx.DefaultSize,
        style=wx.DEFAULT_FRAME_STYLE,
        name="frame",
    ):
        super(MeshFrame, self).__init__(parent, id, title, pos, size, style, name)
        self.GLinitialized = False
        attribList = (
            glcanvas.WX_GL_RGBA,  # RGBA
            glcanvas.WX_GL_DOUBLEBUFFER,  # Double Buffered
            glcanvas.WX_GL_DEPTH_SIZE,
            24,
        )  # 24 bit

        # Create the canvas
        self.canvas = glcanvas.GLCanvas(self, attribList=attribList)
        self.context = glcanvas.GLContext(self.canvas)

        # Set the event handlers.
        self.canvas.Bind(wx.EVT_ERASE_BACKGROUND, self.processEraseBackgroundEvent)
        self.canvas.Bind(wx.EVT_SIZE, self.processSizeEvent)
        self.canvas.Bind(wx.EVT_PAINT, self.processPaintEvent)
        self.canvas.Bind(wx.EVT_MOUSEWHEEL, self.processMouseWheelEvent)
        self.canvas.Bind(wx.EVT_LEFT_DOWN, self.processLeftDownEvent)
        self.canvas.Bind(wx.EVT_LEFT_UP, self.processLeftUpEvent)
        self.canvas.Bind(wx.EVT_MOTION, self.processMotionEvent)
        self.canvas.Bind(wx.EVT_MIDDLE_UP, self.processMiddleUpEvent)
        self.canvas.Bind(wx.EVT_MIDDLE_DOWN, self.processMiddleDownEvent)

        # wx context
        self.dc = wx.ClientDC(self)

        # create a menu bar
        # self.makeMenuBar()

        # mesh display properties
        self.curve_points = 12

        # data to be drawn
        self.vertex_data = np.array([])
        self.colour_data = np.array([])
        self.num_vertices = 0
        self.buildMesh(mesh)
        self.vertex_buffer = 0
        self.colour_buffer = 0

        # view parameters
        # relative margins to display around the mesh in the default view
        self.margins = 0.05
        # when zooming in by one step, the field of view is multiplied by this value
        self.zoom_factor = 0.95
        # sets self.mesh_limits
        self.setLimits(mesh)
        # current limits
        self.limits = self.mesh_limits.copy()
        self.target_limits = self.mesh_limits.copy()

        # motion state
        self.moving = False
        self.motion_origin = (0.0, 0.0)

        # and a status bar
        # self.CreateStatusBar()
        # self.SetStatusText("initialised")

    # Canvas Proxy Methods

    def GetGLExtents(self):
        """Get the extents of the OpenGL canvas."""
        return self.canvas.GetClientSize()

    def SwapBuffers(self):
        """Swap the OpenGL buffers."""
        self.canvas.SwapBuffers()

    def OnExit(self, event):
        """Close the frame, terminating the application."""
        self.Close(True)

    # wxPython Window Handlers

    def processEraseBackgroundEvent(self, event):
        """Process the erase background event."""
        pass  # Do nothing, to avoid flashing on MSWin

    def processSizeEvent(self, event):
        """Process the resize event."""
        if self.context:
            # Make sure the frame is shown before calling SetCurrent.
            self.Show()
            self.canvas.SetCurrent(self.context)

            # update the view limits
            self.updateLimits()
            self.canvas.Refresh(False)
        event.Skip()

    def processPaintEvent(self, event):
        """Process the drawing event."""
        self.canvas.SetCurrent(self.context)

        # This is a 'perfect' time to initialize OpenGL ... only if we need to
        if not self.GLinitialized:
            self.OnInitGL()
            self.GLinitialized = True

        self.OnDraw()
        event.Skip()

    def processMouseWheelEvent(self, event):
        """
        Processes mouse wheel events.
        Zooms when the vertical mouse wheel is used.
        """

        # vertical or horizontal wheel axis
        axis = event.GetWheelAxis()
        # position of the pointer in pixels in the window frame
        xcp, ycp = event.GetLogicalPosition(self.dc).Get()
        increment = event.GetWheelRotation() / event.GetWheelDelta()
        if axis == wx.MOUSE_WHEEL_VERTICAL:
            self.zoom(xcp, ycp, increment)

    def pixelsToMeshUnits(self, xcp, ycp):
        """
        Given a position in pixels in the window, returns the
        corresponding position in mesh units.
        """

        xmin, xmax, ymin, ymax = self.limits
        size = self.GetGLExtents()
        # xcp is 0 on the left, ycp is zero on the top
        xc = xmin + (xmax - xmin) * xcp / size.width
        yc = ymax - (ymax - ymin) * ycp / size.height
        return (xc, yc)

    def zoom(self, xcp, ycp, increment):
        """
        Zooms around the given centre proportionally to the increment.
        Zooms in if `increment` is positive, out if it is negative.
        The centre (xcp, ycp) is given in pixels, not in mesh units.
        """

        factor = self.zoom_factor**increment
        xmin, xmax, ymin, ymax = self.limits
        xmin_t, xmax_t, ymin_t, ymax_t = self.target_limits
        # get the centre location in mesh units
        xc, yc = self.pixelsToMeshUnits(xcp, ycp)
        # update the limits
        xmin = xc + factor * (xmin - xc)
        xmax = xc + factor * (xmax - xc)
        ymin = yc + factor * (ymin - yc)
        ymax = yc + factor * (ymax - yc)
        xmin_t = xc + factor * (xmin_t - xc)
        xmax_t = xc + factor * (xmax_t - xc)
        ymin_t = yc + factor * (ymin_t - yc)
        ymax_t = yc + factor * (ymax_t - yc)
        self.limits = [xmin, xmax, ymin, ymax]
        self.target_limits = [xmin_t, xmax_t, ymin_t, ymax_t]
        self.updateLimits()
        self.OnDraw()

    def processLeftDownEvent(self, event):
        """
        Process actions that should be done when there is a left click
        """

        # enable view motion mode
        self.moving = True
        # store the position of the click to track how much we're moving the view
        xcp, ycp = event.GetLogicalPosition(self.dc).Get()
        self.motion_origin = self.pixelsToMeshUnits(xcp, ycp)

    def processLeftUpEvent(self, event):
        """
        Process actions that should be done when the left mouse button is released
        """

        # stop dragging the view
        self.moving = False

    def processMiddleDownEvent(self, event):
        """
        Process actions that should be done when there is a middle click
        """
        # enable view motion mode
        print("middle down")
        self.moving = True
        # store the position of the click to track how much we're moving the view
        xcp, ycp = event.GetLogicalPosition(self.dc).Get()
        self.motion_origin = self.pixelsToMeshUnits(xcp, ycp)

    def processMiddleUpEvent(self, event):
        """
        Process actions that should be done when the middle mouse button is released
        """
        print("middle up")
        # stop dragging the view
        self.moving = False

    def processMotionEvent(self, event):
        if self.moving:
            xcp, ycp = event.GetLogicalPosition(self.dc).Get()
            xc, yc = self.pixelsToMeshUnits(xcp, ycp)
            dx = xc - self.motion_origin[0]
            dy = yc - self.motion_origin[1]
            self.target_limits[0] -= dx
            self.target_limits[1] -= dx
            self.target_limits[2] -= dy
            self.target_limits[3] -= dy
            self.updateLimits()
            self.OnDraw()

    # GLFrame OpenGL Event Handlers

    def OnInitGL(self):
        """Initialize OpenGL for use in the window."""
        self.createBuffers()
        gl.glClearColor(1, 1, 1, 1)

    def updateLimits(self):
        """Update the view limits based on the dimensions of the window."""

        size = self.GetGLExtents()
        width = size.width
        height = size.height
        xmin = self.target_limits[0]
        xmax = self.target_limits[1]
        ymin = self.target_limits[2]
        ymax = self.target_limits[3]
        # check whether the view is limited by width or height, and scale accordingly
        lx = xmax - xmin
        ly = ymax - ymin
        if lx / width > ly / height:
            y0 = 0.5 * (ymin + ymax)
            dy = height / width * lx / 2
            ymin = y0 - dy
            ymax = y0 + dy
        else:
            x0 = 0.5 * (xmin + xmax)
            dx = width / height * ly / 2
            xmin = x0 - dx
            xmax = x0 + dx
        self.limits = [xmin, xmax, ymin, ymax]
        gl.glViewport(0, 0, width, height)
        gl.glMatrixMode(gl.GL_PROJECTION)
        gl.glLoadIdentity()
        gl.glOrtho(xmin, xmax, ymin, ymax, -1, 1)

        gl.glMatrixMode(gl.GL_MODELVIEW)
        gl.glLoadIdentity()

    def createBuffers(self):
        # new vertex buffer
        self.vertex_buffer = gl.glGenBuffers(1)
        gl.glBindBuffer(gl.GL_ARRAY_BUFFER, self.vertex_buffer)
        # send the vertex data to the buffer
        gl.glBufferData(gl.GL_ARRAY_BUFFER, self.vertex_data, gl.GL_STATIC_DRAW)
        # unbind the buffer
        gl.glBindBuffer(gl.GL_ARRAY_BUFFER, 0)

    def OnDraw(self, *args, **kwargs):
        "Draw the window."

        # initialise
        gl.glClear(gl.GL_COLOR_BUFFER_BIT)
        gl.glClear(gl.GL_DEPTH_BUFFER_BIT)
        gl.glClearColor(1, 1, 1, 1)
        gl.glEnable(gl.GL_LINE_SMOOTH)
        gl.glLineWidth(1.0)
        gl.glEnableClientState(gl.GL_VERTEX_ARRAY)
        gl.glColor(0, 0, 0)
        # load buffers
        gl.glBindBuffer(gl.GL_ARRAY_BUFFER, self.vertex_buffer)
        gl.glVertexPointer(3, gl.GL_DOUBLE, 0, None)
        gl.glBindBuffer(gl.GL_ARRAY_BUFFER, 0)
        # draw the mesh
        gl.glDrawArrays(gl.GL_LINES, 0, self.num_vertices)
        # finalise
        gl.glDisableClientState(gl.GL_VERTEX_ARRAY)

        self.SwapBuffers()

    def buildMesh(self, mesh):
        """
        Builds the edges to be drawn based on the mesh representation.
        """

        # gives the indices of the vertices of an element in a position array
        def vertex_indices(iface):
            if iface == 0:
                return (0, 0)
            elif iface == 1:
                return (0, -1)
            elif iface == 2:
                return (-1, -1)
            else:
                return (-1, 0)

        current_point = 0
        first_point = 0
        vertices = []
        edges = []
        for el in mesh.elem:
            first_point = current_point
            for iface in range(4):
                j0, i0 = vertex_indices(iface)
                if el.ccurv[iface] == "":
                    vertices.append(
                        (
                            el.pos[0, 0, j0, i0],
                            el.pos[1, 0, j0, i0],
                            0.0,
                        )
                    )
                    if iface < 3:
                        next_point = current_point + 1
                    else:
                        next_point = first_point
                    edges.append((current_point, next_point))
                    current_point += 1
                elif el.ccurv[iface] == "m":
                    # we should draw a parabola passing through the current vertex, the midpoint, and the next vertex.
                    x0, y0 = el.pos[0:2, 0, j0, i0]
                    xm, ym = el.curv[iface][0:2]
                    j1, i1 = vertex_indices((iface + 1) % 4)
                    x1, y1 = el.pos[0:2, 0, j1, i1]
                    # quadratic Lagrange interpolation between points
                    for ipt in range(self.curve_points):
                        # tp varies between 0 and 1
                        tp = ipt / self.curve_points
                        xp = (
                            x0 * 2 * (tp - 0.5) * (tp - 1)
                            - xm * 4 * tp * (tp - 1)
                            + x1 * 2 * tp * (tp - 0.5)
                        )
                        yp = (
                            y0 * 2 * (tp - 0.5) * (tp - 1)
                            - ym * 4 * tp * (tp - 1)
                            + y1 * 2 * tp * (tp - 0.5)
                        )
                        vertices.append((xp, yp, 0))
                        if iface == 3 and ipt == self.curve_points - 1:
                            next_point = first_point
                        else:
                            next_point = current_point + 1
                        edges.append((current_point, next_point))
                        current_point += 1
                elif el.ccurv[iface] == "C":
                    # draw a circle of given radius passing through the next vertex and the current one
                    # first, find the distance between the midpoint of the segment ((x0, y0), (x1, y1)) and the center (xc, yc) of the circle
                    radius = el.curv[iface][
                        0
                    ]  # this can be positive or negative depending on direction
                    x0, y0 = el.pos[0:2, 0, j0, i0]
                    j1, i1 = vertex_indices((iface + 1) % 4)
                    x1, y1 = el.pos[0:2, 0, j1, i1]
                    # length of the segment
                    ls2 = (x1 - x0) ** 2 + (y1 - y0) ** 2
                    try:
                        dist = radius * sqrt(1 - ls2 / (4 * radius**2))
                    except ValueError:
                        raise ValueError("the radius of the curved edge is too small")
                    # midpoint of the edge
                    xm = 0.5 * (x0 + x1)
                    ym = 0.5 * (y0 + y1)
                    # outward normal direction
                    ls = sqrt(ls2)
                    nx = (y1 - y0) / ls
                    ny = -(x1 - x0) / ls
                    # position of the centre
                    xc = xm - nx * dist
                    yc = ym - ny * dist
                    # now find the range of arguments spanned by the circle arc
                    # argument to the centre of the edge
                    theta0 = atan2(ym - yc, xm - xc)
                    dtheta = asin(ls / (2 * radius))
                    theta_min = theta0 - dtheta
                    # Now, add the points
                    for itheta in range(self.curve_points):
                        theta = theta_min + 2 * dtheta * itheta / self.curve_points
                        xp = xc + abs(radius) * cos(theta)
                        yp = yc + abs(radius) * sin(theta)
                        vertices.append((xp, yp, 0))
                        if iface == 3 and itheta == self.curve_points - 1:
                            next_point = first_point
                        else:
                            next_point = current_point + 1
                        edges.append((current_point, next_point))
                        current_point += 1

        # put everything into a buffer that OpenGL can read
        self.num_vertices = 2 * len(edges)
        self.colour_data = np.array([0 for _ in range(4 * self.num_vertices)])
        vertex_data = []
        for edge in edges:
            for vertex in edge:
                x, y, z = vertices[vertex]
                vertex_data.append(x)
                vertex_data.append(y)
                vertex_data.append(z)
        self.vertex_data = np.array(vertex_data)

    def setLimits(self, mesh):
        """
        set view limits to the size of the mesh with some margin
        """
        xmin, xmax = mesh.lims.pos[0]
        ymin, ymax = mesh.lims.pos[1]
        lx = xmax - xmin
        ly = ymax - ymin
        self.mesh_limits = [
            xmin - self.margins * lx,
            xmax + self.margins * lx,
            ymin - self.margins * ly,
            ymax + self.margins * ly,
        ]


def plot2D(mesh):
    # make a new app & frame
    app = wx.App()
    frame = MeshFrame(mesh, None, -1, title="pymech")

    frame.Show()

    # Start the event loop.
    app.MainLoop()

1	import wx	×
2	from wx import glcanvas	×
3	import OpenGL.GL as gl	×
4	import numpy as np	×
5	from math import sqrt, atan2, asin, cos, sin	×
6
7
8	class MeshFrame(wx.Frame):	×
9	"""
10	A frame to display meshes
11	"""
12
13	def __init__(	×
14	self,
15	mesh,
16	parent,
17	id,
18	title,
19	pos=wx.DefaultPosition,
20	size=wx.DefaultSize,
21	style=wx.DEFAULT_FRAME_STYLE,
22	name="frame",
23	):
24	super(MeshFrame, self).__init__(parent, id, title, pos, size, style, name)	×
25	self.GLinitialized = False	×
26	attribList = (	×
27	glcanvas.WX_GL_RGBA, # RGBA
28	glcanvas.WX_GL_DOUBLEBUFFER, # Double Buffered
29	glcanvas.WX_GL_DEPTH_SIZE,
30	24,
31	) # 24 bit
32
33	# Create the canvas
34	self.canvas = glcanvas.GLCanvas(self, attribList=attribList)	×
35	self.context = glcanvas.GLContext(self.canvas)	×
36
37	# Set the event handlers.
38	self.canvas.Bind(wx.EVT_ERASE_BACKGROUND, self.processEraseBackgroundEvent)	×
39	self.canvas.Bind(wx.EVT_SIZE, self.processSizeEvent)	×
40	self.canvas.Bind(wx.EVT_PAINT, self.processPaintEvent)	×
41	self.canvas.Bind(wx.EVT_MOUSEWHEEL, self.processMouseWheelEvent)	×
42	self.canvas.Bind(wx.EVT_LEFT_DOWN, self.processLeftDownEvent)	×
43	self.canvas.Bind(wx.EVT_LEFT_UP, self.processLeftUpEvent)	×
44	self.canvas.Bind(wx.EVT_MOTION, self.processMotionEvent)	×
45	self.canvas.Bind(wx.EVT_MIDDLE_UP, self.processMiddleUpEvent)	×
46	self.canvas.Bind(wx.EVT_MIDDLE_DOWN, self.processMiddleDownEvent)	×
47
48	# wx context
49	self.dc = wx.ClientDC(self)	×
50
51	# create a menu bar
52	# self.makeMenuBar()
53
54	# mesh display properties
55	self.curve_points = 12	×
56
57	# data to be drawn
58	self.vertex_data = np.array([])	×
59	self.colour_data = np.array([])	×
60	self.num_vertices = 0	×
61	self.buildMesh(mesh)	×
62	self.vertex_buffer = 0	×
63	self.colour_buffer = 0	×
64
65	# view parameters
66	# relative margins to display around the mesh in the default view
67	self.margins = 0.05	×
68	# when zooming in by one step, the field of view is multiplied by this value
69	self.zoom_factor = 0.95	×
70	# sets self.mesh_limits
71	self.setLimits(mesh)	×
72	# current limits
73	self.limits = self.mesh_limits.copy()	×
74	self.target_limits = self.mesh_limits.copy()	×
75
76	# motion state
77	self.moving = False	×
78	self.motion_origin = (0.0, 0.0)	×
79
80	# and a status bar
81	# self.CreateStatusBar()
82	# self.SetStatusText("initialised")
83
84	# Canvas Proxy Methods
85
86	def GetGLExtents(self):	×
87	"""Get the extents of the OpenGL canvas."""
88	return self.canvas.GetClientSize()	×
89
90	def SwapBuffers(self):	×
91	"""Swap the OpenGL buffers."""
92	self.canvas.SwapBuffers()	×
93
94	def OnExit(self, event):	×
95	"""Close the frame, terminating the application."""
96	self.Close(True)	×
97
98	# wxPython Window Handlers
99
100	def processEraseBackgroundEvent(self, event):	×
101	"""Process the erase background event."""
102	pass # Do nothing, to avoid flashing on MSWin	×
103
104	def processSizeEvent(self, event):	×
105	"""Process the resize event."""
106	if self.context:	×
107	# Make sure the frame is shown before calling SetCurrent.
108	self.Show()	×
109	self.canvas.SetCurrent(self.context)	×
110
111	# update the view limits
112	self.updateLimits()	×
113	self.canvas.Refresh(False)	×
114	event.Skip()	×
115
116	def processPaintEvent(self, event):	×
117	"""Process the drawing event."""
118	self.canvas.SetCurrent(self.context)	×
119
120	# This is a 'perfect' time to initialize OpenGL ... only if we need to
121	if not self.GLinitialized:	×
122	self.OnInitGL()	×
123	self.GLinitialized = True	×
124
125	self.OnDraw()	×
126	event.Skip()	×
127
128	def processMouseWheelEvent(self, event):	×
129	"""
130	Processes mouse wheel events.
131	Zooms when the vertical mouse wheel is used.
132	"""
133
134	# vertical or horizontal wheel axis
135	axis = event.GetWheelAxis()	×
136	# position of the pointer in pixels in the window frame
137	xcp, ycp = event.GetLogicalPosition(self.dc).Get()	×
138	increment = event.GetWheelRotation() / event.GetWheelDelta()	×
139	if axis == wx.MOUSE_WHEEL_VERTICAL:	×
140	self.zoom(xcp, ycp, increment)	×
141
142	def pixelsToMeshUnits(self, xcp, ycp):	×
143	"""
144	Given a position in pixels in the window, returns the
145	corresponding position in mesh units.
146	"""
147
148	xmin, xmax, ymin, ymax = self.limits	×
149	size = self.GetGLExtents()	×
150	# xcp is 0 on the left, ycp is zero on the top
151	xc = xmin + (xmax - xmin) * xcp / size.width	×
152	yc = ymax - (ymax - ymin) * ycp / size.height	×
153	return (xc, yc)	×
154
155	def zoom(self, xcp, ycp, increment):	×
156	"""
157	Zooms around the given centre proportionally to the increment.
158	Zooms in if `increment` is positive, out if it is negative.
159	The centre (xcp, ycp) is given in pixels, not in mesh units.
160	"""
161
162	factor = self.zoom_factor**increment	×
163	xmin, xmax, ymin, ymax = self.limits	×
164	xmin_t, xmax_t, ymin_t, ymax_t = self.target_limits	×
165	# get the centre location in mesh units
166	xc, yc = self.pixelsToMeshUnits(xcp, ycp)	×
167	# update the limits
168	xmin = xc + factor * (xmin - xc)	×
169	xmax = xc + factor * (xmax - xc)	×
170	ymin = yc + factor * (ymin - yc)	×
171	ymax = yc + factor * (ymax - yc)	×
172	xmin_t = xc + factor * (xmin_t - xc)	×
173	xmax_t = xc + factor * (xmax_t - xc)	×
174	ymin_t = yc + factor * (ymin_t - yc)	×
175	ymax_t = yc + factor * (ymax_t - yc)	×
176	self.limits = [xmin, xmax, ymin, ymax]	×
177	self.target_limits = [xmin_t, xmax_t, ymin_t, ymax_t]	×
178	self.updateLimits()	×
179	self.OnDraw()	×
180
181	def processLeftDownEvent(self, event):	×
182	"""
183	Process actions that should be done when there is a left click
184	"""
185
186	# enable view motion mode
187	self.moving = True	×
188	# store the position of the click to track how much we're moving the view
189	xcp, ycp = event.GetLogicalPosition(self.dc).Get()	×
190	self.motion_origin = self.pixelsToMeshUnits(xcp, ycp)	×
191
192	def processLeftUpEvent(self, event):	×
193	"""
194	Process actions that should be done when the left mouse button is released
195	"""
196
197	# stop dragging the view
198	self.moving = False	×
199
200	def processMiddleDownEvent(self, event):	×
201	"""
202	Process actions that should be done when there is a middle click
203	"""
204	# enable view motion mode
205	print("middle down")	×
206	self.moving = True	×
207	# store the position of the click to track how much we're moving the view
208	xcp, ycp = event.GetLogicalPosition(self.dc).Get()	×
209	self.motion_origin = self.pixelsToMeshUnits(xcp, ycp)	×
210
211	def processMiddleUpEvent(self, event):	×
212	"""
213	Process actions that should be done when the middle mouse button is released
214	"""
215	print("middle up")	×
216	# stop dragging the view
217	self.moving = False	×
218
219	def processMotionEvent(self, event):	×
220	if self.moving:	×
221	xcp, ycp = event.GetLogicalPosition(self.dc).Get()	×
222	xc, yc = self.pixelsToMeshUnits(xcp, ycp)	×
223	dx = xc - self.motion_origin[0]	×
224	dy = yc - self.motion_origin[1]	×
225	self.target_limits[0] -= dx	×
226	self.target_limits[1] -= dx	×
227	self.target_limits[2] -= dy	×
228	self.target_limits[3] -= dy	×
229	self.updateLimits()	×
230	self.OnDraw()	×
231
232	# GLFrame OpenGL Event Handlers
233
234	def OnInitGL(self):	×
235	"""Initialize OpenGL for use in the window."""
236	self.createBuffers()	×
237	gl.glClearColor(1, 1, 1, 1)	×
238
239	def updateLimits(self):	×
240	"""Update the view limits based on the dimensions of the window."""
241
242	size = self.GetGLExtents()	×
243	width = size.width	×
244	height = size.height	×
245	xmin = self.target_limits[0]	×
246	xmax = self.target_limits[1]	×
247	ymin = self.target_limits[2]	×
248	ymax = self.target_limits[3]	×
249	# check whether the view is limited by width or height, and scale accordingly
250	lx = xmax - xmin	×
251	ly = ymax - ymin	×
252	if lx / width > ly / height:	×
253	y0 = 0.5 * (ymin + ymax)	×
254	dy = height / width * lx / 2	×
255	ymin = y0 - dy	×
256	ymax = y0 + dy	×
257	else:
258	x0 = 0.5 * (xmin + xmax)	×
259	dx = width / height * ly / 2	×
260	xmin = x0 - dx	×
261	xmax = x0 + dx	×
262	self.limits = [xmin, xmax, ymin, ymax]	×
263	gl.glViewport(0, 0, width, height)	×
264	gl.glMatrixMode(gl.GL_PROJECTION)	×
265	gl.glLoadIdentity()	×
266	gl.glOrtho(xmin, xmax, ymin, ymax, -1, 1)	×
267
268	gl.glMatrixMode(gl.GL_MODELVIEW)	×
269	gl.glLoadIdentity()	×
270
271	def createBuffers(self):	×
272	# new vertex buffer
273	self.vertex_buffer = gl.glGenBuffers(1)	×
274	gl.glBindBuffer(gl.GL_ARRAY_BUFFER, self.vertex_buffer)	×
275	# send the vertex data to the buffer
276	gl.glBufferData(gl.GL_ARRAY_BUFFER, self.vertex_data, gl.GL_STATIC_DRAW)	×
277	# unbind the buffer
278	gl.glBindBuffer(gl.GL_ARRAY_BUFFER, 0)	×
279
280	def OnDraw(self, args, *kwargs):	×
281	"Draw the window."
282
283	# initialise
284	gl.glClear(gl.GL_COLOR_BUFFER_BIT)	×
285	gl.glClear(gl.GL_DEPTH_BUFFER_BIT)	×
286	gl.glClearColor(1, 1, 1, 1)	×
287	gl.glEnable(gl.GL_LINE_SMOOTH)	×
288	gl.glLineWidth(1.0)	×
289	gl.glEnableClientState(gl.GL_VERTEX_ARRAY)	×
290	gl.glColor(0, 0, 0)	×
291	# load buffers
292	gl.glBindBuffer(gl.GL_ARRAY_BUFFER, self.vertex_buffer)	×
293	gl.glVertexPointer(3, gl.GL_DOUBLE, 0, None)	×
294	gl.glBindBuffer(gl.GL_ARRAY_BUFFER, 0)	×
295	# draw the mesh
296	gl.glDrawArrays(gl.GL_LINES, 0, self.num_vertices)	×
297	# finalise
298	gl.glDisableClientState(gl.GL_VERTEX_ARRAY)	×
299
300	self.SwapBuffers()	×
301
302	def buildMesh(self, mesh):	×
303	"""
304	Builds the edges to be drawn based on the mesh representation.
305	"""
306
307	# gives the indices of the vertices of an element in a position array
308	def vertex_indices(iface):	×
309	if iface == 0:	×
310	return (0, 0)	×
311	elif iface == 1:	×
312	return (0, -1)	×
313	elif iface == 2:	×
314	return (-1, -1)	×
315	else:
316	return (-1, 0)	×
317
318	current_point = 0	×
319	first_point = 0	×
320	vertices = []	×
321	edges = []	×
322	for el in mesh.elem:	×
323	first_point = current_point	×
324	for iface in range(4):	×
325	j0, i0 = vertex_indices(iface)	×
326	if el.ccurv[iface] == "":	×
327	vertices.append(	×
328	(
329	el.pos[0, 0, j0, i0],
330	el.pos[1, 0, j0, i0],
331	0.0,
332	)
333	)
334	if iface < 3:	×
335	next_point = current_point + 1	×
336	else:
337	next_point = first_point	×
338	edges.append((current_point, next_point))	×
339	current_point += 1	×
340	elif el.ccurv[iface] == "m":	×
341	# we should draw a parabola passing through the current vertex, the midpoint, and the next vertex.
342	x0, y0 = el.pos[0:2, 0, j0, i0]	×
343	xm, ym = el.curv[iface][0:2]	×
344	j1, i1 = vertex_indices((iface + 1) % 4)	×
345	x1, y1 = el.pos[0:2, 0, j1, i1]	×
346	# quadratic Lagrange interpolation between points
347	for ipt in range(self.curve_points):	×
348	# tp varies between 0 and 1
349	tp = ipt / self.curve_points	×
350	xp = (	×
351	x0 * 2 * (tp - 0.5) * (tp - 1)
352	- xm * 4 * tp * (tp - 1)
353	+ x1 * 2 * tp * (tp - 0.5)
354	)
355	yp = (	×
356	y0 * 2 * (tp - 0.5) * (tp - 1)
357	- ym * 4 * tp * (tp - 1)
358	+ y1 * 2 * tp * (tp - 0.5)
359	)
360	vertices.append((xp, yp, 0))	×
361	if iface == 3 and ipt == self.curve_points - 1:	×
362	next_point = first_point	×
363	else:
364	next_point = current_point + 1	×
365	edges.append((current_point, next_point))	×
366	current_point += 1	×
367	elif el.ccurv[iface] == "C":	×
368	# draw a circle of given radius passing through the next vertex and the current one
369	# first, find the distance between the midpoint of the segment ((x0, y0), (x1, y1)) and the center (xc, yc) of the circle
370	radius = el.curv[iface][	×
371	0
372	] # this can be positive or negative depending on direction
373	x0, y0 = el.pos[0:2, 0, j0, i0]	×
374	j1, i1 = vertex_indices((iface + 1) % 4)	×
375	x1, y1 = el.pos[0:2, 0, j1, i1]	×
376	# length of the segment
377	ls2 = (x1 - x0) 2 + (y1 - y0) 2	×
378	try:	×
379	dist = radius * sqrt(1 - ls2 / (4 * radius**2))	×
380	except ValueError:	×
381	raise ValueError("the radius of the curved edge is too small")
382	# midpoint of the edge
383	xm = 0.5 * (x0 + x1)	×
384	ym = 0.5 * (y0 + y1)	×
385	# outward normal direction
386	ls = sqrt(ls2)	×
387	nx = (y1 - y0) / ls	×
388	ny = -(x1 - x0) / ls	×
389	# position of the centre
390	xc = xm - nx * dist	×
391	yc = ym - ny * dist	×
392	# now find the range of arguments spanned by the circle arc
393	# argument to the centre of the edge
394	theta0 = atan2(ym - yc, xm - xc)	×
395	dtheta = asin(ls / (2 * radius))	×
396	theta_min = theta0 - dtheta	×
397	# Now, add the points
398	for itheta in range(self.curve_points):	×
399	theta = theta_min + 2 * dtheta * itheta / self.curve_points	×
400	xp = xc + abs(radius) * cos(theta)	×
401	yp = yc + abs(radius) * sin(theta)	×
402	vertices.append((xp, yp, 0))	×
403	if iface == 3 and itheta == self.curve_points - 1:	×
404	next_point = first_point	×
405	else:
406	next_point = current_point + 1	×
407	edges.append((current_point, next_point))	×
408	current_point += 1	×
409
410	# put everything into a buffer that OpenGL can read
411	self.num_vertices = 2 * len(edges)	×
412	self.colour_data = np.array([0 for _ in range(4 * self.num_vertices)])	×
413	vertex_data = []	×
414	for edge in edges:	×
415	for vertex in edge:	×
416	x, y, z = vertices[vertex]	×
417	vertex_data.append(x)	×
418	vertex_data.append(y)	×
419	vertex_data.append(z)	×
420	self.vertex_data = np.array(vertex_data)	×
421
422	def setLimits(self, mesh):	×
423	"""
424	set view limits to the size of the mesh with some margin
425	"""
426	xmin, xmax = mesh.lims.pos[0]	×
427	ymin, ymax = mesh.lims.pos[1]	×
428	lx = xmax - xmin	×
429	ly = ymax - ymin	×
430	self.mesh_limits = [	×
431	xmin - self.margins * lx,
432	xmax + self.margins * lx,
433	ymin - self.margins * ly,
434	ymax + self.margins * ly,
435	]
436
437
438	def plot2D(mesh):	×
439	# make a new app & frame
440	app = wx.App()	×
441	frame = MeshFrame(mesh, None, -1, title="pymech")	×
442
443	frame.Show()	×
444
445	# Start the event loop.
446	app.MainLoop()	×

eX-Mech / pymech / 3806400180

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