如何在Matlab中繪製3D平面？

Question

我想用我從3個點，其中計算的矢量繪製一個平面：

pointA = [0,0,0]; 
pointB = [-10,-20,10]; 
pointC = [10,20,10]; 

plane1 = cross(pointA-pointB, pointA-pointC) 

如何在3D繪圖「基準面1」？

Answer 1

這裏的陰謀使用fill3飛機一個簡單的方法：

points=[pointA' pointB' pointC']; % using the data given in the question 
fill3(points(1,:),points(2,:),points(3,:),'r') 
grid on 
alpha(0.3) 

Answer 2

您已經計算出的法向量。現在你應該決定你的飛機在x和z的限制，並創建一個矩形的補丁。

解釋：每個平面可用其法向量(A,B,C)和另一個係數D來表徵。這架飛機的方程式是AX+BY+CZ+D=0。跨產品之間兩點之間的差異，cross(P3-P1,P2-P1)允許查找(A,B,C)。爲了找到D，簡單地把任何一點到上面提到的公式：

D = -Ax-By-Cz; 

一旦你有平面的方程，你可以坐4分擺在這個平面上，並得出他們之間的補丁。

normal = cross(pointA-pointB, pointA-pointC); %# Calculate plane normal 
%# Transform points to x,y,z 
x = [pointA(1) pointB(1) pointC(1)]; 
y = [pointA(2) pointB(2) pointC(2)]; 
z = [pointA(3) pointB(3) pointC(3)]; 

%Find all coefficients of plane equation  
A = normal(1); B = normal(2); C = normal(3); 
D = -dot(normal,pointA); 
%Decide on a suitable showing range 
xLim = [min(x) max(x)]; 
zLim = [min(z) max(z)]; 
[X,Z] = meshgrid(xLim,zLim); 
Y = (A * X + C * Z + D)/ (-B); 
reOrder = [1 2 4 3]; 
figure();patch(X(reOrder),Y(reOrder),Z(reOrder),'b'); 
grid on; 
alpha(0.3); 

Answer 3

這就是我想出了：

function [x, y, z] = plane_surf(normal, dist, size) 

normal = normal/norm(normal); 
center = normal * dist; 

tangents = null(normal') * size; 

res(1,1,:) = center + tangents * [-1;-1]; 
res(1,2,:) = center + tangents * [-1;1]; 
res(2,2,:) = center + tangents * [1;1]; 
res(2,1,:) = center + tangents * [1;-1]; 

x = squeeze(res(:,:,1)); 
y = squeeze(res(:,:,2)); 
z = squeeze(res(:,:,3)); 

end 

，你會爲使用：

normal = cross(pointA-pointB, pointA-pointC); 
dist = dot(normal, pointA) 

[x, y, z] = plane_surf(normal, dist, 30); 
surf(x, y, z); 

其中在飛機上繪製邊長爲60的正方形問題

Answer 4

我想補充一下Andrey Rubshtein給出的答案，他的代碼在B = 0時非常好用。這裏是他的代碼編輯後的版本

下面的代碼的工作原理當不爲0

normal = cross(pointA-pointB, pointA-pointC); 
x = [pointA(1) pointB(1) pointC(1)]; 
y = [pointA(2) pointB(2) pointC(2)]; 
z = [pointA(3) pointB(3) pointC(3)]; 
A = normal(1); B = normal(2); C = normal(3); 
D = -dot(normal,pointA); 
zLim = [min(z) max(z)]; 
yLim = [min(y) max(y)]; 
[Y,Z] = meshgrid(yLim,zLim); 
X = (C * Z + B * Y + D)/ (-A); 
reOrder = [1 2 4 3]; 
figure();patch(X(reOrder),Y(reOrder),Z(reOrder),'r'); 
grid on; 
alpha(0.3); 

下面的代碼工作時，C不是0

normal = cross(pointA-pointB, pointA-pointC); 
x = [pointA(1) pointB(1) pointC(1)]; 
y = [pointA(2) pointB(2) pointC(2)]; 
z = [pointA(3) pointB(3) pointC(3)]; 
A = normal(1); B = normal(2); C = normal(3); 
D = -dot(normal,pointA); 
xLim = [min(x) max(x)]; 
yLim = [min(y) max(y)]; 
[Y,X] = meshgrid(yLim,xLim); 
Z = (A * X + B * Y + D)/ (-C); 
reOrder = [1 2 4 3]; 
figure();patch(X(reOrder),Y(reOrder),Z(reOrder),'r'); 
grid on; 
alpha(0.3);