我正在进行光线跟踪，我在世界坐标中描述了一个屏幕为矩阵（我在屏幕坐标中的X，Y，Z之前，通过使用变换和旋转，我在世界坐标中得到它）
Xw（NXM矩阵） Yw（NXM矩阵） Zw（我通过拟合3D数据Xw和Yw得到了这个多项式（5阶多项式）。我把它作为f（Xw，Yw））
我的光线方程也像往常一样描述：
X = Ox + t*Dx
Y = Oy + t*Dy
Z = Oz + t*Dz %(O is the origin point and D is the direction)
所以我所做的就是我用多项式方程f（Xw，Yw）替换了X和Y并将其求解为t，这样我就可以得到交点。
但显然我使用的方法是错误的（我得到的交叉点在其他地方）。
任何人都可以帮助我，告诉我这是什么错误。请支持我。
由于
这是代码的一部分：
X_World_coordinate_scr = ScreenXCoordinates.*Rotation_matrix_screen(1,1) + ScreenYCoordinates.*Rotation_matrix_screen(1,2) + ScreenZCoordinates.*Rotation_matrix_screen(1,3) + Zerobase_scr(1);
Y_World_coordinate_scr = ScreenXCoordinates.*Rotation_matrix_screen(2,1) + ScreenYCoordinates.*Rotation_matrix_screen(2,2) + ScreenZCoordinates.*Rotation_matrix_screen(2,3) + Zerobase_scr(2);
Z_World_coordinate_scr = ScreenXCoordinates.*Rotation_matrix_screen(3,1) + ScreenYCoordinates.*Rotation_matrix_screen(3,2) + ScreenZCoordinates.*Rotation_matrix_screen(3,3) + Zerobase_scr(3); % converting the screen coordinates to the world coordinates using the rotation matrix and the translation vector
polymodel = polyfitn([X_World_coordinate_scr(:),Y_World_coordinate_scr(:)],Z_World_coordinate_scr(:),5); % using a function from the MAtlab file exchange and I trust this function. I tried it different data and it gives me the f(Xw,Yw).
ScreenPoly = polyn2sym(polymodel); % Function from Matlab file exchange to give the symbolic shape of the polynomial.
syms X Y Z t Dx Ox Dy Oy oz Dz z;
tsun = matlabFunction(LayerPoly, 'vars',[X,Y,Z]); % just to substitue the symboles from X , Y and Z to (Ox+t*Dx) , (Oy+t*Dy) and (Oz+t*Dz) respectively
Equation = tsun((Ox+t*Dx),(Oy+t*Dy),(Oz+t*Dz));
Answer = solve(Equation,t); % solving it for t but the equation that it is from the 5th order and the answer is RootOf(.... for z)
a = char(Answer); % preparing it to find the roots (Solutions of t)
R = strrep(a,'RootOf(','');
R1 = strrep(R,', z)','');
b = sym(R1);
PolyCoeffs = coeffs(b,z); % get the coefficient of the polynomail
tfun = matlabFunction(PolyCoeffs, 'vars',[Ox,Oy,oz,Dx,Dy,Dz]);
tCounter = zeros(length(Directions),1);
NaNIndices = find(isnan(Surface(:,1))==1); %I have NaN values and I am taking them out
tCounter(NaNIndices) = NaN;
NotNaNIndices = find(isnan(Surface(:,1))==0);
for i = NotNaNIndices' % for loop to calc
OxNew = Surface(i,1);
OyNew = Surface(i,2);
OzNew = Surface(i,3);
DxNew = Directions(i,1);
DyNew = Directions(i,2);
DzNew = Directions(i,3);
P = tfun(OxNew,OyNew,OzNew ,DxNew,DyNew,DzNew);
t = roots(P);
t(imag(t) ~= 0) = []; % getting rid of the complex solutions
tCounter(i) = t;
end
请支持
提前致谢