用3d點創建平面

Question

下面的代碼定義了法向量和平面的半徑以便可視化它。我的問題是關於d和偏移量。是d從平面方程D Ax+By+Cz+D=0（因爲我必須給d，我沒有找到一個與該代碼）？該代碼將幫助我定義3D點是在飛機的前/後，左側還是右側。 任何反饋，這將有助於我理解這一點，非常感謝。

**function [fixture,n,min_radius] = planePointPoint(p1,p2,p3,q,d,varargin)** 

% p1, p2 and p3 -3d points that define an oriented plane. 
%q is the point that is tested against this plane 
% p1+offset is the fixture point for the plane. 
% d is the offset distance for the plane in the direction of n. 
% optional argument offset is a 3-vector denoting an offset to be added to the fixture point during min_radius calculation 
% 
% function returns sequence of fixture points and unit normals along with 
% minimum radii that make sense to visualize position of q in relation to the plane. 
offset = [0;0;0]; 
if (nargin>6) 
    offset = varargin{1}; 
end 
n = cross(p1 - p3,p2 - p3);%defines normal vector 
n = n./repmat(sqrt(sum(n.^2)),3,1);%normalise normal vector 
offset = repmat(offset,1,mot.nframes) - repmat(dot(n,repmat(offset,1,mot.nframes)),3,1).*n; 
%points = p1 + n*d; 
fixture = p1+offset + n*d; 
dist_q = dot(n,q-fixture); 
dist_p1 = dot(n,p1-fixture); 
dist_p2 = dot(n,p2-fixture); 
dist_p3 = dot(n,p3-fixture); 
q_proj = q - repmat(dist_q,3,1).*n; 
p1_proj = p1 - repmat(dist_p1,3,1).*n; 
p2_proj = p2 - repmat(dist_p2,3,1).*n; 
p3_proj = p3 - repmat(dist_p3,3,1).*n; 
radius_q = sqrt(sum((fixture-q_proj).^2)); 
radius_p1 = sqrt(sum((fixture-p1_proj).^2)); 
radius_p2 = sqrt(sum((fixture-p2_proj).^2)); 
radius_p3 = sqrt(sum((fixture-p3_proj).^2)); 
min_radius = max([radius_q; radius_p1; radius_p2; radius_p3]); 

Answer 1

我不明白究竟這是什麼代碼是幹什麼的，但它似乎是d（這是該行fixture = p1+offset + n*d;使用）必須是起源和由三個點定義的平面之間的距離簽署。如果您用等式Ax+By+Cz+D=0來描述您的飛機，其中(A,B,C)是代碼中描述的正常單位矢量n，那麼d = - D。

如果這是正確的，那麼誰寫這段代碼是特別惡從來電者問d，因爲它可以從其它輸入來計算：

d = dot(n,p1); 

關於您的實際問題（The code will help me define if a 3D point is above/down, in front/behind, left/right of a plane.），簡單地使用以下兩行：

n = cross(p1 - p3,p2 - p3); 
h = dot(n,q-p1); 

如果h是空值，則q屬於平面，如果是正，則它是平面的上方，而如果它是負，則它下面是。這裏，「以上」是指如果您從q看到飛機，則順序逆時針循環，順序爲p1→p2→p3→p1。