Calculate the required area
显示 更早的评论
I would like to paint a building (all 5 surfaces) that has 4 vertical straight walls, the upper surface (roof) is described by the function z = g (x, y) for (x, y) ∈ [0.0,4.40] × [0.0, 4.20]. The lower edge of the building is at a height of z (x, y) ≡0. Calculate the required area.
This is the area I would like to calculate
I tried to calculate like this but it does not get me the right answer. Any help?
g = @(x, y) 1./((2+1.1.*x.^2+1.1.*y.^2).^(1/2));
a=0.0;
b=4.40;
c=0.0;
d=4.20;
s1= 1./((2+1.1.*(0.0).^2+1.1.*(0.0).^2).^(1/2));
s2= 1./((2+1.1.*(4.40).^2+1.1.*(4.20).^2).^(1/2));
s3= 1./((2+1.1.*(0.0).^2+1.1.*(4.20).^2).^(1/2));
s4= 1./((2+1.1.*(4.40).^2+1.1.*(0.0).^2).^(1/2));
roof = integral2(g,a,b,c,d);
wall1 = integral2(g,a,b,0,s1);
wall2 = integral2(g,a,b,0,s2);
wall3 = integral2(g,c,d,0,s3);
wall4 = integral2(g,c,d,0,s4);
area = roof + wall1 + wall2 + wall3 + wall4;
1 个评论
Riccardo Scorretti
2022-4-30
In this way you are computing volumes, not surfaces. The problem is with mathematics, not with MATLAB.
采纳的回答
Riccardo Scorretti
2022-4-30
编辑：Riccardo Scorretti
2022-4-30
Let's start by checking the function g = profile of your building:
g = @(x, y) 1./((2+1.1.*x.^2+1.1.*y.^2).^(1/2));
a=0.0;
b=4.40;
c=0.0;
d=4.20;
[x, y] = meshgrid(a:0.4:b, c:0.4:d);
figure ; mesh(x, y, g(x,y)) ; axis image ; grid on ;
axis([a, b, c, d, 0 inf]);
camproj perspective ; box on
xlabel('x') ; ylabel('y');
For the 4 walls, the computation boils up into a simple 1D integral:
wall1 = integral(@(x) g(x,c), a, b)
wall3 = integral(@(x) g(x,d), a, b)
and
wall2 = integral(@(y) g(a,y), c, d)
wall4 = integral(@(y) g(b,y), c, d)
The case of the roof is quite different: it is a 2D integral of the surface given defined by the map 
, that is:
, that is:
Assuming that g is given as a numerical function (and not analytically), the derivatives must be computed numerically as well, for instance by finite difference. This will introduce some numerical error, which will be quite negligible if the surface is smooth enough:
dx = 1.0E-5 ; dy = dx;
gx = @(x,y) (g(x+dx,y) - g(x-dx,y))/(2*dx);
gy = @(x,y) (g(x,y+dy) - g(x,y-dy))/(2*dy);
roof = integral2(@(x,y) sqrt(1 + gx(x,y).^2 + gy(x,y).^2), a, b, c, d)
The bottom line is:
tot = wall1 + wall2 + wall3 + wall4 + roof
更多回答（0 个）
类别
在 帮助中心 和 File Exchange 中查找有关 Triangulations 的更多信息
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!
Translated by 
