Matlab

Question

我想使用一些条件 space 填充 3D 区域。

假设有这样一个向量：

x1 = 100;
y1 = 102;
z1 = 103;
P1 = [x1, y1, z1];

现在我想为 P2 = [x2, y2, z2]; 的所有可能值指明 space，例如：

x2 < x1;
y2 < y1;
z2 < z1;
x1 - x2 < y1 - y2;
y1 - y2 < z1 - z2;
|angle between P1 and P2| < pi/20

我认为 fill3 功能不起作用。

我试过绘制所有可能的点，但是速度很慢：

r1 = 100;
g1 = 102;
b1 = 103;

P1 = [r1, g1, b1];

for r2 = 0:0.1:r1
    for g2 = 0:0.1:g1
        for b2=0:0.1:b1

            % calculate angle between two vectors
            P2 = [r2, g2, b2];
            a = abs(atan2(norm(cross(P1,P2)),dot(P1,P2)));
            
            % draw point if conditions are true
            if ((b1 - b2) < (g1 - g2)) && ((g1 - g2) <= (r1 - r2)) && (a < (pi/20)) 
                scatter3(r2,g2,b2,5,'g');
                hold on;
            end
            
        end
    end
end

我如何应用这些条件并为 P2 的所有可能值填充 3D space 区域？

Answer 1

您通过单独调用 scatter3 来绘制每个点。相反，您应该首先执行计算并找到点，然后一次绘制它们：

r1 = 100; g1 = 102; b1 = 103;
P1 = [r1, g1, b1];
step = .5;
r = 0:step:r1;
g = 0:step:g1;
b = 0:step:b1;
[R, G, B] = meshgrid(r, g, b);
n = numel(R);
inside = false(size(R));
for ii= 1:n
    r2 = R(ii);
    g2 = G(ii);
    b2 = B(ii);
    
    % calculate angle between two vectors
    P2 = [r2, g2, b2];
    a = abs(atan2(norm(cross(P1,P2)),dot(P1,P2)));
    
    % draw point if conditions are true
    if ((b1 - b2) < (g1 - g2)) && ((g1 - g2) <= (r1 - r2)) && (a < (pi/20))
        inside(ii) = true;
    end
end
scatter3(R(inside), G(inside), B(inside), 5, 'g');

另外，如果你对图解体积感兴趣，可以调用convhull求出点的凸厅：

k = convhull(R(inside), G(inside), B(inside));
trisurf(k,R(inside), G(inside), B(inside), 'facecolor', 'g', 'edgealpha', .1)

你甚至可以简化凸包：

k = convhull(R(inside), G(inside), B(inside),'Simplify',true);

编辑：添加透明度

您可以通过设置 'MarkerEdgeAlpha' 属性使您的散点图透明。然而，它可能不会改变结果，除了体积的边缘。那是因为有太多标记互相覆盖了:

subplot 131
scatter3(R(inside), G(inside), B(inside), 5, 'r');
axis equal, title('solid')

subplot 132
scatter3(R(inside), G(inside), B(inside), 5, 'r', ...
    'markeredgealpha', 0.1);
axis equal, title('transparent')

subplot 133
scatter3(R(inside), G(inside), B(inside), 5, 'r', ...
    'markeredgealpha', 0.1);
axis equal, title('zoomed'), zoom(4)

您还可以将冲浪对象设为透明：

subplot 121
trisurf(k,R(inside), G(inside), B(inside), 'facecolor', 'g', ...
    'edgealpha', 0.1)
axis equal, title('solid')

subplot 122
trisurf(k,R(inside), G(inside), B(inside), 'facecolor', 'g', ...
    'facealpha', 0.3, 'edgealpha', .1)
axis equal, title('transparent')

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