triangle.py

from numpy import array, cross, dot
from PyQt4.QtCore import Qt
from PyQt4.QtGui import QApplication, QWidget, QPainter, QTransform, QBrush, QColor
import sys
from itertools import izip


def cycle_list(lst, skip=0):
    for i in lst[skip:]:
        yield i
    while True:
        for i in lst:
            yield i


colours = cycle_list([Qt.lightGray, Qt.darkGreen, Qt.darkBlue, Qt.darkGray, Qt.darkRed, Qt.yellow])


class Widget(QWidget):
    def __init__(self):
        QWidget.__init__(self)

        self.triangle = []
        self.np_triangle = []
        self.points = []
        self.normal = []

    def is_inside(self, point):
        point = array([point.x(), point.y(), 0])

        x = dot(cross(self.np_triangle[1] - self.np_triangle[0], point - self.np_triangle[0]), self.normal)
        print 'x', x
        if x < 0:
            return False

        y = dot(cross(point - self.np_triangle[0], self.np_triangle[2] - self.np_triangle[0]), self.normal)
        print 'y', y
        if y < 0:
            return False

        if dot(cross(self.np_triangle[2] - self.np_triangle[1], point - self.np_triangle[1]), self.normal) < 0:
            return False

        return True

    def paintEvent(self, event):
        painter = QPainter(self)
        painter.scale(self.width(), self.height())
        for a, b in izip(self.triangle, cycle_list(self.triangle, skip=1)):
            painter.drawLine(a, b)

        for point in self.points:
            painter.setBrush(QBrush(QColor(Qt.green if self.is_inside(point) else Qt.red)))
            painter.drawEllipse(point, 0.005, 0.005)

    def mouseReleaseEvent(self, event):
        transform = QTransform()
        transform.scale(self.width(), self.height())
        transform = transform.inverted()[0]
        if len(self.triangle) < 3:
            point = transform.map(event.posF())
            self.triangle.append(point)
            self.np_triangle.append(array([point.x(), point.y(), 0]))
            if len(self.np_triangle) == 3:
                self.normal = cross(self.np_triangle[1] - self.np_triangle[0], self.np_triangle[2] - self.np_triangle[0])
                print 'normal', self.normal
        else:
            self.points.append(transform.map(event.posF()))
        self.repaint()


app = QApplication(sys.argv)

widget = Widget()
widget.show()

app.exec_()