我正在尝试使用 MATLAB 测试包围体算法（光线追踪之前）背后的数学。
到目前为止，我已经成功地创建了相对简单的轴对齐包围体，并且我相信我已经成功地创建了包围球。
然后我尝试创建一个与对象对齐的边界体积——但尽管我相信我的主轴是正确的，因为盒子看起来是一个合适的形状——但我无法将它正确地“翻译”到形状上。
本质上我的问题是 - 我在我的算法中做错了什么以及如何将我的边界体积转换为形状。
我一直在使用的两个来源是Maths for 3D Games，以及一个博客，它给出了一些关于进行翻译的指示 - 但似乎效果不佳。
我已将我的源代码放在下面 - 非常感谢！
%//===================Declare vertices and faces===================
vp_vtx = [379.379,684.302,319.752,711.497,215.956,439.237,600,600,732.938,418.084,600,600,747.081;
225.836,158.305,394.208,337.480,84.834,245.958,212.858,342.251,322.344,330.576,300,416.190,398.885;
0.933,0.917,0.904,0.878,0.854,0.923,0.914,0.949,0.943,0.908,0.896,0.940,0.933;
1,1,1,1,1,1,1,1,1,1,1,1,1];
ws_fcs = [2,4,3,6,6,7,7,10,10; %//Faces forming shape
4,3,1,7,11,9,13,11,13;
5,5,5,11,10,13,11,13,12];
%//===================Create an AA bounding box===================
x = vp_vtx(1,:);y = vp_vtx(2,:);z = vp_vtx(3,:); %//Seperate vertex coordinates
bb_vtx = [min(x),max(x),min(x),max(x),min(x),max(x),min(x),max(x); %//Take min/max from each
min(y),min(y),max(y),max(y),min(y),min(y),max(y),max(y); %//To form enclosing box
min(z),min(z),min(z),min(z),max(z),max(z),max(z),max(z)];
bb_fcs = [1,2,6,1,1,3; 2,4,5,5,2,4;4,8,7,7,6,8; 3,6,8,3,5,7]; %//Allocate faces of box
figure(); grid on; hold on; xlabel('x'); ylabel('y'); zlabel('z');
scatter3(vp_vtx(1,:),vp_vtx(2,:),vp_vtx(3,:),'r'); %//Plot shape
patch('Faces',ws_fcs','Vertices',vp_vtx(1:3,:)', 'Facecolor', 'r','FaceAlpha', 0.1)
patch('Faces',bb_fcs', 'Vertices',bb_vtx','FaceColor','g','FaceAlpha', 0.05);%//Plot enclosing box
mean_point = sum(vp_vtx,2)/length(vp_vtx);
C = zeros(4,4); %//Create 4x4 empty matrix
for i = 1:length(vp_vtx)
C = C+(vp_vtx(:,i)-mean_point)*(vp_vtx(:,i)-mean_point)'; %//Sum to get covarience matrix
end;
C = C/length(vp_vtx); %//Scale by the number of samples
[y,v] = eig(C(1:3,1:3)) ;%//Get eigenvalues & eigen vectors
R = y(:,1); %//Eigen vectors & values form object aligned axes
S = y(:,2);
T = y(:,3);%//T is principle axis as derived from largest eigenvalue
%//========Create an Object Orientated Bounding Box=========
dot_arr = zeros(size(vp_vtx));
for i = 1:length(vp_vtx) %//Create array of dot products with each OO axis
dot_arr(1,i) = dot(vp_vtx(1:3,i),T);
dot_arr(2,i) = dot(vp_vtx(1:3,i),R);
dot_arr(3,i) = dot(vp_vtx(1:3,i),S);
end
%//Get min/max variation in each OO axis
a = 0.5*(min(dot_arr(1,:)) + max(dot_arr(1,:)));
b = 0.5*(min(dot_arr(2,:)) + max(dot_arr(2,:)));
c = 0.5*(min(dot_arr(3,:)) + max(dot_arr(3,:)));
%//Centre is point where the 3 planes of the box intersect? (from book)
q = a*T + b*R + c*S;
Tr = vertcat(horzcat(T,S,R,q),[0,0,0,1]); %//Transform & translate original AA box
bb_vtx = Tr*vertcat(bb_vtx, ones(1,length(bb_vtx)));
patch('Faces',bb_fcs', 'Vertices',bb_vtx(1:3,:)','FaceColor','g','FaceAlpha', 0.05);