Matlab绘制视锥体/截锥

发表于 分类于 Waline：
本文字数： 1.7k 阅读时长 ≈ 2 分钟

DrawFrustum.m

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
% 1.输入六个面的表达式
% 每个面由4个参数决定: ax + by + cx + d = 0
%       left,     right,     bottom,   top,      far,       near
as = [ -0.138808  0.997943   0.336104  0.234905  0.666782  -0.666782  ];
bs = [ -0.053909 -0.053909   0.864693 -0.936352 -0.0836785  0.0836785 ];
cs = [  0.988851 -0.0346808  0.373283  0.26089   0.74054   -0.74054   ];
ds = [  2.78514   3.55528    0.726959  3.48709  -5.07915    95.0791   ];

% 2.求交点
% 每3个面交于一点，共8个顶点
ids = [ % 面的索引
  1, 4, 6;
  2, 4, 6;
  1, 4, 5;
  2, 4, 5;
  1, 3, 6;
  2, 3, 6;
  1, 3, 5;
  2, 3, 5;
];
corners = zeros(8, 3); % 保存8个交点的x、y、z
for i = (1:8)
    % 取3个面
    ps = [ids(i, 1), ids(i, 2), ids(i, 3)]; 
    % 3个面的a、b、c、d
    a = [as(ps(1)), as(ps(2)), as(ps(3))];
    b = [bs(ps(1)), bs(ps(2)), bs(ps(3))];
    c = [cs(ps(1)), cs(ps(2)), cs(ps(3))];
    d = [ds(ps(1)), ds(ps(2)), ds(ps(3))];
    
    % 解三元一次方程组
    A1 = a(2)*b(1)-a(1)*b(2);
    B1 = a(2)*c(1)-a(1)*c(2);
    C1 = a(2)*d(1)-a(1)*d(2);
    A2 = a(2)*b(3)-a(3)*b(2);
    B2 = a(2)*c(3)-a(3)*c(2);
    C2 = a(2)*d(3)-a(3)*d(2);
    z = (-C1*A2+C2*A1)/(B1*A2-B2*A1);
    y = (-C1-B1*z)/A1;
    x = (-d(1)-b(1)*y-c(1)*z)/a(1);
    
    corners(i, 1) = x;
    corners(i, 2) = y;
    corners(i, 3) = z;
end
%corners

% 3.由交点绘制平面
% 每4个点组成一个面，共6个面
ids = [ % 点的索引
  1, 5, 7, 3; % left
  2, 6, 8, 4; % right
  5, 6, 8, 7; % bottom
  1, 2, 4, 3; % top
  3, 4, 8, 7; % far
  1, 2, 6, 5; % near
];
colors = ['r', 'g', 'b', 'y', 'w', 'k']; % 6个面的颜色
for i = (1:6)
    % 取4个点
    ps = [ids(i, 1), ids(i, 2), ids(i, 3), ids(i, 4)];
    % 4个点的x、y、z
    xs = [corners(ps(1), 1), corners(ps(2), 1), corners(ps(3), 1), corners(ps(4), 1)];
    ys = [corners(ps(1), 2), corners(ps(2), 2), corners(ps(3), 2), corners(ps(4), 2)];
    zs = [corners(ps(1), 3), corners(ps(2), 3), corners(ps(3), 3), corners(ps(4), 3)];

    fill3(xs, ys, zs, colors(i));
    hold on
end

% 设置坐标轴
xlabel("X");
ylabel("Y");
zlabel("Z");
axis equal;

因为使用的是右手系中的数据，所以颜色顺序不太对