matlab对点云进行三角化(las格式读入)
1、LASread_and_convert.m文件（运行这个文件实现las读入为mat文件)
clear;
clc;
close all;
clear all;
A = LASreadAll('house_wall.las');%调用函数读取las文件
Point_City = [A.x,A.y,A.z];
save Point_City.mat;
%将X1_buny赋值给一个p
p = Point_City;
%显示点云
figure(1);
hold on
axis equal
title('点云','fontsize',14)
plot3(p(:,1),p(:,2),p(:,3),'g.')%这里颜色如果是 ‘r’就不行？？？
view(-37.5,30)
[t]=MyCrust(p);
%% plot of the oyput triangulation
figure(2)
hold on
title('三角化输出','fontsize',14)
axis equal
trimesh(t,p(:,1),p(:,2),p(:,3),'edgecolor','b')%plot della superficie trattata
view(-37.5,30)2、LASreadAll函数
function A = LASreadAll(infilename)
% LASREADALL reads in all variables from a LAS 1.x data file (used with lidar data)
%
% INPUT
% infilename: input file name (for example, 'myinfile.las')
%
% OUTPUT
% A: This is a structure containing all the data in the file.
% See the file documentation for more information:
% http://www.asprs.org/Committee-General/LASer-LAS-File-Format-Exchange-Activities.html
%
% EXAMPLE
% A = LASreadAll('infile.las')
%
% Cici Alexander
% September 2008 (updated 26.09.2008)
% Amy Farris (afarris@usgs.gov)
% November 2013 Substatially altered to read in all variables from the file
% This file has the capability to load data files using any 1 of 5 formats.
% However, I was only able to test it with one of the formats.
% I included support for the rest of the file formats b/c I
% thought someone might find it useful. I sure hope they work!!!
% If the code crashes, it may be because either the pointDataFormatID
% value was not what I expected, or the value for pointDataRecordLength
% is not what I think it should be based on the format ID.
% If pointDataRecordLength is different than I expected, then you may need
% to change the values in fseek, eg: (c+????)
% The number added to c should be the sum of bytes of all the variables
% that occur before the variable currently being read in.
%
% Also, the file I tested this code with was LAS format 1.2, I
% think this code will run on later versions of LAS.
%
% A brief explanation of the LAS file format:
% LAS files are binary, they begin with header information. Included in
% the header is the size of the header (in bytes); this is called
% 'OffsetToPointData', refered to a 'c' in this code. After c bytes the
% data begins with the first x value, then the first y value and so on...
% (exactly what data is included depends on the file format). Then the
% file continues with the second x value, the second y value and so on...
% The header tells you how many bytes of data there are for each data point
% ('pointDataRecordLength', also refered to as 'p' in this code).
% So to read in all the x values, you start at the beginig of the file and
% skip c bytes: "(fseek(fid, c, 'bof');"
% Then you read in one value and skip p-4 bytes
% (each x value consists of 4 bytes) and then read the next x and so on:
% "X1 = fread(fid,inf,'int32',p-4);"
%
% This is my (Amy Farris') first attempt at reading in a binary file.
% I depended strongly on Cici's orignal file (LASRead.m) at first. Most
% of the code after about line # 134 was written by me, as are these
% garrolous beginning comments. I hope they help.
%% Open the file
fid =fopen(infilename);
% Check whether the file is valid
if fid == -1
error('Error opening file')
end
%% Read in important information from the header
% Check whether the LAS format is 1.1
fseek(fid, 24, 'bof');
VersionMajor = fread(fid,1,'uchar');
VersionMinor = fread(fid,1,'uchar');
% afarris2011Aug20 changed the following line to read LAS1.2 files
% if VersionMajor ~= 1 || VersionMinor ~= 1
if VersionMajor ~= 1
error('LAS format is not 1.*')
end
% Read in the offset to point data
fseek(fid, 96, 'bof');
OffsetToPointData = fread(fid,1,'uint32');
% Read in the point data fotmat ID
fseek(fid, 104, 'bof');
pointDataFormatID = fread(fid,1,'uchar');
% Read in the point data record length
fseek(fid, 105, 'bof');
pointDataRecordLength = fread(fid,1,'short');
% Read in the scale factors and offsets required to calculate the coordinates
fseek(fid, 131, 'bof');
XScaleFactor = fread(fid,1,'double');
YScaleFactor = fread(fid,1,'double');
ZScaleFactor = fread(fid,1,'double');
XOffset = fread(fid,1,'double');
YOffset = fread(fid,1,'double');
ZOffset = fread(fid,1,'double');
% The number of bytes from the beginning of the file to the first point record
% data field is used to access the attributes of the point data
c = OffsetToPointData;
% The number of bytes to skip after reading in each value is based on
% 'pointDataRecordLength' So I need a short version of the variable name:
p = pointDataRecordLength;
%% Now read in the data
% Reads in the X coordinates of the points; making use of the
% XScaleFactor and XOffset values in the header.
fseek(fid, c, 'bof');
X1 = fread(fid,inf,'int32',p-4);
A.x = X1*XScaleFactor+XOffset;
% Read in the Y coordinates of the points
fseek(fid, c+4, 'bof');
Y1 = fread(fid,inf,'int32',p-4);
A.y = Y1*YScaleFactor+YOffset;
% Read in the Z coordinates of the points
fseek(fid, c+8, 'bof');
Z1 = fread(fid,inf,'int32',p-4);
A.z = Z1*ZScaleFactor+ZOffset;
% Read in the Intensity values of the points
fseek(fid, c+12, 'bof');
A.intensity = fread(fid,inf,'uint16',p-2);
% Read in the Return Number of the points. The first return will have a
% return number of one, the second, two, etc.
% In the next two fread's, p needs to be in bits = 8*byte
fseek(fid, c+14, 'bof');
A.ReturnNumber = fread(fid,inf,'bit3',p*8-3);
% Read in the Number of Returns for a given pulse.
fseek(fid, c+14, 'bof');
fread(fid,1,'bit3');
A.NumberOfReturns = fread(fid,inf,'bit3',p*8-3);
% Read in classification
fseek(fid, c+15, 'bof');
A.classification = fread(fid,inf,'char',p-1);
% Read in scan angle Rank
fseek(fid, c+16, 'bof');
A.scanAngleRank = fread(fid,inf,'char',p-1);
A.scanAngleRankInfo = '-90 to 90 left side';
% Read in User ID
fseek(fid, c+17, 'bof');
A.userID = fread(fid,inf,'char',p-1);
% Read in Point SourceID
fseek(fid, c+18, 'bof');
A.pointSourceID = fread(fid,inf,'short',p-2);
%% Now read in data specific to certain file formats
% Remembeber, only the code that reads in format 1 was tested
switch pointDataFormatID
case 1
if pointDataRecordLength ~= 28
error('pointDataRecordLength is not what i expected')
end
% Read in 'Global Encoding', which tells us what the time variable is
fseek(fid, 6, 'bof');
globalEncoding = fread(fid,1,'short');
if globalEncoding
A.timeInfo = 'Time is "standard GPS time minus 1e9"';
disp('Time is "standard GPS time minus 1e9"')
else
A.timeIinfo = 'Time is second of the GPS Week; and NO, we do not know WHICH week. ';
disp('Time is second of the GPS Week; and NO, we do not know WHICH week. ')
end
% Read in time
fseek(fid, c+20, 'bof');
A.time = fread(fid,inf,'double',p-8);
case 2
if pointDataRecordLength ~= 26
error('pointDataRecordLength is not what i expected')
end
% Read in color
fseek(fid, c+20, 'bof');
A.red = fread(fid,inf,'short',p-2);
fseek(fid, c+22, 'bof');
A.green = fread(fid,inf,'short',p-2);
fseek(fid, c+24, 'bof');
A.blue = fread(fid,inf,'short',p-2);
case 3
if pointDataRecordLength ~= 34
error('pointDataRecordLength is not what i expected')
end
% Read in 'Global Encoding', which tells us what the time variable is
fseek(fid, 6, 'bof');
globalEncoding = fread(fid,1,'short');
if globalEncoding
A.timeInfo = 'Time is "standard GPS time minus 1e9"';
disp('Time is "standard GPS time minus 1e9"')
else
A.timeInfo = 'Time is second of the GPS Week; and NO, we do not know WHICH week. ';
disp('Time is second of the GPS Week; and NO, we do not know WHICH week. ')
end
% Read in time
fseek(fid, c+20, 'bof');
A.time = fread(fid,inf,'double',p-8);
% Read in color
fseek(fid, c+28, 'bof');
A.red = fread(fid,inf,'short',p-2);
fseek(fid, c+30, 'bof');
A.green = fread(fid,inf,'short',p-2);
fseek(fid, c+32, 'bof');
A.blue = fread(fid,inf,'short',p-2);
case 4
if pointDataRecordLength ~= 57
error('pointDataRecordLength is not what i expected')
end
% Read in 'Global Encoding', which tells us what the time variable is
fseek(fid, 6, 'bof');
globalEncoding = fread(fid,1,'short');
if globalEncoding
A.timeInfo = 'Time is "standard GPS time minus 1e9"';
disp('Time is "standard GPS time minus 1e9"')
else
A.timeInfo = 'Time is second of the GPS Week; and NO, we do not know WHICH week. ';
disp('Time is second of the GPS Week; and NO, we do not know WHICH week. ')
end
% Read in time
fseek(fid, c+20, 'bof');
A.time = fread(fid,inf,'double',p-8);
fseek(fid, c+28, 'bof');
A.wavePacketDescriptorIndex = fread(fid,inf,'char',p-1);
fseek(fid, c+29, 'bof');
% i am not sure that 'unit64' is correct below
A.byteOffsettoWaveformData = fread(fid,inf,'unit64',p-8);
fseek(fid, c+37, 'bof');
A.waveformPacketSize = fread(fid,inf,'unit32',p-4);
A.waveformPacketSizeInfo = 'in bytes';
fseek(fid, c+41, 'bof');
% i am not sure that 'float' is correct below
A.returnPointWaveformLocation = fread(fid,inf,'float',p-4);
fseek(fid, c+45, 'bof');
A.Xt = fread(fid,inf,'float',p-4);
fseek(fid, c+49, 'bof');
A.Yt = fread(fid,inf,'float',p-4);
fseek(fid, c+53, 'bof');
A.Zt = fread(fid,inf,'float',p-4);
case 5
if pointDataRecordLength ~= 63
error('pointDataRecordLength is not what i expected')
end
% Read in 'Global Encoding', which tells us what the time variable is
fseek(fid, 6, 'bof');
globalEncoding = fread(fid,1,'short');
if globalEncoding
A.timeInfo = 'Time is "standard GPS time minus 1e9"';
disp('Time is "standard GPS time minus 1e9"')
else
A.timeInfo = 'Time is second of the GPS Week; and NO, we do not know WHICH week. ';
disp('Time is second of the GPS Week; and NO, we do not know WHICH week. ')
end
% Read in time
fseek(fid, c+20, 'bof');
A.time = fread(fid,inf,'double',p-8);
% Read in color
fseek(fid, c+28, 'bof');
A.red = fread(fid,inf,'short',p-2);
fseek(fid, c+30, 'bof');
A.green = fread(fid,inf,'short',p-2);
fseek(fid, c+32, 'bof');
A.blue = fread(fid,inf,'short',p-2);
fseek(fid, c+34, 'bof');
A.wavePacketDescriptorIndex = fread(fid,inf,'char',p-1);
fseek(fid, c+35, 'bof');
% i am not sure that 'unit64' is correct below
A.byteOffsettoWaveformData = fread(fid,inf,'unit64',55);
fseek(fid, c+43, 'bof');
A.waveformPacketSize = fread(fid,inf,'unit32',p-4);
A.waveformPacketSizeInfo = 'in bytes';
fseek(fid, c+47, 'bof');
% i am not sure that 'float' is correct below
A.returnPointWaveformLocation = fread(fid,inf,'float',p-4);
fseek(fid, c+51, 'bof');
A.Xt = fread(fid,inf,'float',p-4);
fseek(fid, c+53, 'bof');
A.Yt = fread(fid,inf,'float',p-4);
fseek(fid, c+57, 'bof');
A.Zt = fread(fid,inf,'float',p-4);
end3、MyCrust函数
%% MyCrust
%
%Simple surface recostruction program based on Crust algorithm
%Given a set of 3D points returns a triangulated tight surface.
%
%The more points there are the best the surface will be fitted,
%although you will have to wait more. For very large models an
%help memory errors may occurs.
%It is important even the point distribution, generally uniformly
% distributed points with denser zones in high curvature features
% give the best results.
%
% Remember crust algorithom needs a cloud representing a volume
% so open surface may give inaccurate results.
%
%
% If any problems occurs in execution, or if you found a bug,
% have a suggestion or question just contact me at:
%
% giaccariluigi@msn.com
%
%
%
%
%Here is a simple example:
%
%load Dino.mat%load input points from mat file
%
%[t]=MyCrust(p);
%
% figure(1)
% hold on
% title('Output Triangulation','fontsize',14)
% axis equal
% trisurf(t,p(:,1),p(:,2),p(:,3),'facecolor','c','edgecolor','b')
%
%Input:
% p is a Nx3 array containing the 3D set of points
%Output:
% t are points id contained in triangles Nx3 array too.
%
% See also qhull, voronoin, convhulln, delaunay, delaunay3, tetramesh.
%
%Author:Giaccari Luigi
%Last Update: 1/12/2008
%Creation: 10/10/2008
function [t]=MyCrust(p)
%% Main
starttime=clock;
%add points to the given ones, this is usefull
%to create outside tetraedrom
tic
p=AddShield(p);
fprintf('Addedded Shield: %4.4f s\n',toc)
tic
tetr=delaunayn(p);%creating tedraedron
tetr=int32(tetr);%use integer to save memory
fprintf('Delaunay Triangulation Time: %4.4f s\n',toc)
%connectivity data
%find triangles to tetraedrom and tetraedrom to triangles connectivity data
tic
[t2tetr,tetr2t]=Connectivity(tetr);
fprintf('Connectivity Time: %4.4f s\n',toc)
tic
[cc,r]=CC();%Circumcenters of tetraedroms
fprintf('Circumcenters Time: %4.4f s\n',toc)
clear n
tic
t=Walking();%Flagging tetraedroms as inside or outside
fprintf('Walking Time: %4.4f s\n',toc)
time=etime(clock,starttime);
fprintf('Total Time: %4.4f s\n',time)
%% Circumcenters(Nested)
function [cc,r]=CC()
%finds circumcenters fro a set of tetraedrom
%points of tetraedrom
p1=(p(tetr(:,1),:));
p2=(p(tetr(:,2),:));
p3=(p(tetr(:,3),:));
p4=(p(tetr(:,4),:));
%vectors of tetraedrom edges
v21=p(tetr(:,1),:)-p(tetr(:,2),:);
v31=p(tetr(:,3),:)-p(tetr(:,1),:);
v41=p(tetr(:,4),:)-p(tetr(:,1),:);
%preallocation
cc=zeros(size(tetr,1),3);
%Solve the system using cramer method
d1=sum(v41.*(p1+p4)*.5,2);
d2=sum(v21.*(p1+p2)*.5,2);
d3=sum(v31.*(p1+p3)*.5,2);
det23=(v21(:,2).*v31(:,3))-(v21(:,3).*v31(:,2));
det13=(v21(:,3).*v31(:,1))-(v21(:,1).*v31(:,3));
det12=(v21(:,1).*v31(:,2))-(v21(:,2).*v31(:,1));
Det=v41(:,1).*det23+v41(:,2).*det13+v41(:,3).*det12;
detx=d1.*det23+...
v41(:,2).*(-(d2.*v31(:,3))+(v21(:,3).*d3))+...
v41(:,3).*((d2.*v31(:,2))-(v21(:,2).*d3));
dety=v41(:,1).*((d2.*v31(:,3))-(v21(:,3).*d3))+...
d1.*det13+...
v41(:,3).*((d3.*v21(:,1))-(v31(:,1).*d2));
detz=v41(:,1).*((v21(:,2).*d3)-(d2.*v31(:,2)))...
+v41(:,2).*(d2.*v31(:,1)-v21(:,1).*d3)...
+d1.*(det12);
%Circumcenters
cc(:,1)=detx./Det;
cc(:,2)=dety./Det;
cc(:,3)=detz./Det;
%Circumradius
r=((sum((p2-cc).^2,2))).^.5;%quadrato del raggio
end
%% Connectivity(Nested)
function [t2tetr,tetr2t]=Connectivity(tetr)
numt = size(tetr,1);
vect = 1:numt;
t = [tetr(:,[1,2,3]); tetr(:,[2,3,4]); tetr(:,[1,3,4]);tetr(:,[1,2,4])];%triangles not unique
[t,j,j] = unique(sort(t,2),'rows');%triangles
t2tetr = [j(vect), j(vect+numt), j(vect+2*numt),j(vect+3*numt)];%each tetraedrom has 3 triangles
% triang-to-tetr connectivity
nume = size(t,1);
tetr2t = zeros(nume,2,'int32');
count= ones(nume,1,'int8');
for k = 1:numt
for j=1:4
ce = t2tetr(k,j);
tetr2t(ce,count(ce)) = k;
count(ce)=count(ce)+1;
end
end
end % connectivity()
%% Walking(Nested)
function t=Walking()
np=size(p,1)-540;%540 = number of shield points put at the end of array
numtetr=size(tetr,1);
nt=size(tetr2t,1);
deleted=true(numtetr,1);%deleted tetraedroms
checked=false(numtetr,1);%checked tetraedros
onfront=false(nt,1);%tetraedroms that need to be checked
countchecked=0;
%First flag as outsde tetraedroms with Shield points
for i=1:numtetr
for j=1:4
if tetr(i,j)>np;
deleted(i)=true;
checked(i)=true;
onfront(t2tetr(i,:))=true;
countchecked=countchecked+1;
break
end
end
end
%tollerances to mark as in or out
toll=zeros(nt,1)+.95;
level=0;
alpha=zeros(nt,1);%intersection factor
%it is computed from radius of the tetraedroms circumscribed sphere
% and the distance between their center
for i=1:nt
if tetr2t(i,2)>0 %jump boundary tetraedrom
distcc=sum((cc(tetr2t(i,1),:)-cc(tetr2t(i,2),:)).^2,2);%distance from circumcenters
%intersection factor
alpha(i)=(-distcc+r(tetr2t(i,1))^2+r(tetr2t(i,2))^2)/(2*r(tetr2t(i,1))*r(tetr2t(i,2)));
end
end
clear cc
% Now we scan all tetraedroms. When one is scanned put on front is
% neighobur. This means that now even the neighobour can be
% checked. At the begining only tetraedroms with shield points are
% on front, because we are sure the are out.
% Tetraedrom with high intersction factor will be marked as equal
% else different.
% When I say high i mean under a set tollerance that becames lower as the algorithm
% progresses. This Aims to avoid errors propagation when a tetraedrom is wrong marked.
%
while countchecked<numtetr && level<50
level=level+1;%level of scan reached
for id=1:nt%loop trough triangles
if onfront(id)
tetr1=tetr2t(id,1);tetr2=tetr2t(id,2);%tetraedroms linked to triangle under analysis
if tetr2==0 %do not check boundary triangles
onfront(id)=false;
continue
elseif (checked(tetr1) && checked(tetr2)) %tetraedroms are already checked
onfront(id)=false;
continue
end
if alpha(id)>=toll(id) %flag as equal
if checked(tetr1)%find the checked one between the two
deleted(tetr2)=deleted(tetr1) ;%flag as equal
checked(tetr2)=true;%check
countchecked=countchecked+1;
onfront(t2tetr(tetr2,:))=true;%put on front all tetreadrom triangles
else
deleted(tetr1)=deleted(tetr2) ;%flag as equal
checked(tetr1)=true;%check
countchecked=countchecked+1;
onfront(t2tetr(tetr1,:))=true;%put on front all tetreadrom triangles
end
onfront(id)=false;%remove from front
elseif alpha(id)<-toll(id)%flag as different
if checked(tetr1)%find the checked one between the two
deleted(tetr2)=~(deleted(tetr1)) ;%flag as different
checked(tetr2)=true;%check
countchecked=countchecked+1;
onfront(t2tetr(tetr2,:))=true;%put on front all tetreadrom triangles
else
deleted(tetr1)=~(deleted(tetr2)) ;%flag as different
checked(tetr1)=true;%check
countchecked=countchecked+1;
onfront(t2tetr(tetr1,:))=true;%put on front all tetreadrom triangles
end
onfront(id)=false;%remove from front
else
toll(id)=toll(id)-.05;%tolleraces were too high next time will be lower
end
end
end
if level==31 %brute continuation(this may appens when the triangulation is corrupt)
warning('Brute continuation necessary')
onfront(t2tetr(~(checked),:))=true;%force onfront collocation
end
end
%delete tetraedroms marked as outside
tetr(deleted,:)=[];
%take boundary triangles from tetraedroms
%this is the raw surface and needs improvements to be used in CAD
%systems. Maybe in my next revision I will add surface post treatments.
%Anyway for grafical purpose this should be good.
%extract boundary triangles
t=BoundTriangles(tetr);
%Output Data
numchecked=countchecked/numtetr;
if level==50
warning([num2str(level),' th level was reached\n'])
else
fprintf('%4.4f th level was reached\n',level)
end
fprintf('%4.4f %% of Tetraedrom were checked\n',numchecked*100)
end
end
%% AddAddShield
function pnew=AddShield(p)
%find the bounding box
maxx=max(p(:,1));
maxy=max(p(:,2));
maxz=max(p(:,3));
minx=min(p(:,1));
miny=min(p(:,2));
minz=min(p(:,3));
%give offset to the bounding box
step=max(abs([maxx,minx,maxy,miny,maxz,minz]));
maxx=maxx+step;
maxy=maxy+step;
maxz=maxz+step;
minx=minx-step;
miny=miny-step;
minz=minz-step;
step=step/100;
N=10;
%creating a grid lying on the bounding box
vx=linspace(minx,maxx,N);
vy=linspace(miny,maxy,N);
vz=linspace(minz,maxz,N);
[x,y]=meshgrid(vx,vy);
facez1=[x(:),y(:),ones(N*N,1)*maxz];
facez2=[x(:),y(:),ones(N*N,1)*minz];
[x,y]=meshgrid(vy,vz-step);
facex1=[ones(N*N,1)*maxx,x(:),y(:)];
facex2=[ones(N*N,1)*minx,x(:),y(:)];
[x,y]=meshgrid(vx-step,vz);
facey1=[x(:),ones(N*N,1)*maxy,y(:)];
facey2=[x(:),ones(N*N,1)*miny,y(:)];
%add points to the p array
pnew=[p;
facex1;
facex2;
facey1;
facey2;
facez1;
facez2];
% figure(2)
% plot3(pnew(:,1),pnew(:,2),pnew(:,3),'.g')
end
%% BoundTriangles
function t=BoundTriangles(tetr)
numt = size(tetr,1);
vect = 1:numt;
t = [tetr(:,[1,2,3]); tetr(:,[2,3,4]); tetr(:,[1,3,4]);tetr(:,[1,2,4])];
[t,j,j] = unique(sort(t,2),'rows');
t2tetr = [j(vect), j(vect+numt), j(vect+2*numt),j(vect+3*numt)];
% triang-to-tetr connectivity
% Each row has two entries corresponding to the triangle numbers
% associated with each triangle. Boundary triangles have only one tetraedrom
nume = size(t,1);
tetr2t = zeros(nume,2,'int32');
count= ones(nume,1,'int32');
for k = 1:numt
for j=1:4
ce = t2tetr(k,j);
tetr2t(ce,count(ce)) = k;
count(ce)=count(ce)+1;
end
end
tbound=false(numt,1);
tbound=tetr2t(:,2)==0;
t=t(tbound,:);
end