09 - Interpolação em Triângulos¶

Para essa atividade vamos usar o Numpy e Matplotlib. Assim vamos carregar as bibliotecas.

In [43]:

import numpy as np
import matplotlib
import matplotlib.pyplot as plt
import matplotlib.tri as mtri

import numpy as np import matplotlib import matplotlib.pyplot as plt import matplotlib.tri as mtri

Vamos definir algumas funções auxiliares que vão nos ajudar a exibir os gráficos.

In [44]:

# Faz o setup para desenhar gráficos
def graph():
    fig = plt.figure()
    ax = plt.axes()
    plt.grid()
    ax.set_xlim(-4, 4)
    ax.set_ylim(-4, 4)
    ax.axhline(0, color='black') # deixa o X do eixo 0 em destaque
    ax.axvline(0, color='black') # deixa o Y do eixo 0 em destaque
    ax.set_aspect('equal') # Não suportado em todas as plataformas
    ax.set(xlabel='x', ylabel='y')
    fig.tight_layout()
    return ax

# Fonte: https://stackoverflow.com/questions/41596386/tripcolor-using-rgb-values-for-each-vertex
def colors_to_cmap(colors):
    colors = np.asarray(colors)
    if colors.shape[1] == 3:
        colors = np.hstack((colors, np.ones((len(colors),1))))
    steps = (0.5 + np.asarray(range(len(colors)-1), dtype=float))/(len(colors) - 1)
    return matplotlib.colors.LinearSegmentedColormap(
        'auto_cmap',
        {clrname: ([(0, col[0], col[0])] + 
                   [(step, c0, c1) for (step,c0,c1) in zip(steps, col[:-1], col[1:])] + 
                   [(1, col[-1], col[-1])])
         for (clridx,clrname) in enumerate(['red', 'green', 'blue', 'alpha'])
         for col in [colors[:,clridx]]},
        N=len(colors))

def draw_triangle(poly, colors):
    triangles = np.asarray([[0, 1, 2]])
    triang = mtri.Triangulation(poly[0], poly[1], triangles)
    cmap = colors_to_cmap(colors)
    zs = np.asarray(range(3), dtype=float)/2
    plt.tripcolor(triang, zs, cmap=cmap, shading='gouraud' )
    plt.grid()
    plt.scatter(poly[0], poly[1], s=20, color=colors)

# Faz o setup para desenhar gráficos def graph(): fig = plt.figure() ax = plt.axes() plt.grid() ax.set_xlim(-4, 4) ax.set_ylim(-4, 4) ax.axhline(0, color='black') # deixa o X do eixo 0 em destaque ax.axvline(0, color='black') # deixa o Y do eixo 0 em destaque ax.set_aspect('equal') # Não suportado em todas as plataformas ax.set(xlabel='x', ylabel='y') fig.tight_layout() return ax # Fonte: https://stackoverflow.com/questions/41596386/tripcolor-using-rgb-values-for-each-vertex def colors_to_cmap(colors): colors = np.asarray(colors) if colors.shape[1] == 3: colors = np.hstack((colors, np.ones((len(colors),1)))) steps = (0.5 + np.asarray(range(len(colors)-1), dtype=float))/(len(colors) - 1) return matplotlib.colors.LinearSegmentedColormap( 'auto_cmap', {clrname: ([(0, col[0], col[0])] + [(step, c0, c1) for (step,c0,c1) in zip(steps, col[:-1], col[1:])] + [(1, col[-1], col[-1])]) for (clridx,clrname) in enumerate(['red', 'green', 'blue', 'alpha']) for col in [colors[:,clridx]]}, N=len(colors)) def draw_triangle(poly, colors): triangles = np.asarray([[0, 1, 2]]) triang = mtri.Triangulation(poly[0], poly[1], triangles) cmap = colors_to_cmap(colors) zs = np.asarray(range(3), dtype=float)/2 plt.tripcolor(triang, zs, cmap=cmap, shading='gouraud' ) plt.grid() plt.scatter(poly[0], poly[1], s=20, color=colors)

O código abaixo desenha um triangulo com cores por vértice. Identifique as cores dos 3 pontos de teste (variável prob) usando coordenadas baricêntricas.

In [47]:

ax = graph() # configura o espaço para desenhar um gráfico 2D

# Vértices do triângulo
poly = np.array([[ -2.0,  2.0, 0.0],
                 [ -2.0, -2.0, 1.0]])

# Cores definidas para cada vértice do triângulo
colors = np.asarray( [[1.0,0.0,0.0],
                      [0.0,1.0,0.0], 
                      [0.0,0.0,1.0]] )

# Desenho do triângulo
draw_triangle(poly, colors) # Desenha triângulo colorido

# Pontos de teste
prob = np.array([[ -1.5,  1.5, 0.0],
                 [ -1.5, -1.5, 0.5]])
plt.scatter(prob[0], prob[1], s=20, marker="*", color="black")

plt.show()

ax = graph() # configura o espaço para desenhar um gráfico 2D # Vértices do triângulo poly = np.array([[ -2.0, 2.0, 0.0], [ -2.0, -2.0, 1.0]]) # Cores definidas para cada vértice do triângulo colors = np.asarray( [[1.0,0.0,0.0], [0.0,1.0,0.0], [0.0,0.0,1.0]] ) # Desenho do triângulo draw_triangle(poly, colors) # Desenha triângulo colorido # Pontos de teste prob = np.array([[ -1.5, 1.5, 0.0], [ -1.5, -1.5, 0.5]]) plt.scatter(prob[0], prob[1], s=20, marker="*", color="black") plt.show()