triSurfRayTrace

Below is a demonstration of the features of the triSurfRayTrace function

Syntax
Description
Examples
Example use for ray tracing a single ray or line to multiple faces
Example use for ray tracing of multiple rays or lines to multiple faces
Example input variations
Example use for ray tracing of paired ray-face intersections
Example use for ray tracing of paired line-face intersections

clear; close all; clc;

Syntax

[P,indIntersect,d,TUV]=triSurfRayTrace(P_origin,Nr,F,V,optionStruct);

Description

This function performs ray-tracings using the rays or lines defined by Nr with origin P_origin. The rays are traced to the surface defined by the faces F and the vertices V. An option structure can be added to control the tolerance level to use to consider intersections on ray/line and on triangle.

DEFAULTS: defaultOptionStruct.tolEps = 1e-5; %Tolerance level defaultOptionStruct.triSide = 0; %Triangle sides to consider defaultOptionStruct.rayType = 'ray'; %Use 'ray' type rather than 'line' defaultOptionStruct.exclusionType = 'inclusive'; %Include within tolerance defaultOptionStruct.paired=0;

The output consists of: P : An nx3 array for the intersection point coordinates indIntersect : An nx2 array with indices for rays and faces or the first/second columns respectively. d : An nx1 array with distances from the ray origin to the intersection point TUV : An nx3 array with the t-parameter, and the barycentric coordinates u and v as columns

Examples

Plot settings

markerSize=40;
fontSize=10;
faceAlpha=0.25;

Example triangulated surfaces

[F,V]=geoSphere(1,1);

Example use for ray tracing a single ray or line to multiple faces

This example shows non-paired analysis. This means that intersections are computed for each ray for all faces.

p_origin=[0 0 3];%Ray origin
nr=[0 0 -1]; %Ray vector

optionStruct.tolEps        = 1e-6;
optionStruct.triSide       = 0;
optionStruct.rayType       = 'ray';
optionStruct.exclusionType = 'inclusive';
optionStruct.paired        = 0;

[P,indIntersect,d,TUV]=triSurfRayTrace(p_origin,nr,F,V,optionStruct);

Visualization

p_end=p_origin+nr;

cFigure; hold on;
title([optionStruct.rayType,' / triSide: ',num2str(optionStruct.triSide)])
gpatch(F,V,'w','k',faceAlpha);
hp(1)=gpatch(F(indIntersect(:,2),:),V,'kw','k',1,1);
hp(2)=patchNormPlot(F,V,[],'f','g');
hp(3)=quiverVec(p_origin,nr,[],'b');

hp(4)=plotV(P,'r.','MarkerSize',markerSize);
legend(hp,{'Intersected faces','Normal directions','Ray/Line points','Intersection points'},'Location','SouthOutSide')

clear hp;
axisGeom(gca,fontSize); axis off;
camlight headlight;
drawnow;

Example use for ray tracing of multiple rays or lines to multiple faces

p_origin1=[-0.4 0 2];
p_origin2=[0.4 0 2];
p_origin3=[-1.2 0 2];

nr1=[0 0 -1];
nr2=[0 0 -1];
nr3=[0 0 -1];
nr4=[0 0 -1];
P_origin= [p_origin1; p_origin2; p_origin3]; %Ray line origins
Nr=[nr1; nr2; nr3]; %Ray/line vectors

optionStruct.tolEps        = 1e-6;
optionStruct.triSide       = 0;
optionStruct.rayType       = 'ray';
optionStruct.exclusionType = 'inclusive';
optionStruct.paired        = 0;

[P,indIntersect,d,TUV]=triSurfRayTrace(P_origin,Nr,F,V,optionStruct);

Visualization

cFigure; hold on;
title([optionStruct.rayType,' / triSide: ',num2str(optionStruct.triSide)])
gpatch(F,V,'w','k',faceAlpha,1);
hp(1)=gpatch(F(indIntersect(:,2),:),V,'kw','k',1,1);
hp(2)=patchNormPlot(F,V,[],'f','g');
hp(3)=quiverVec(P_origin,Nr,[],'b');
hp(4)=plotV(P,'r.','MarkerSize',markerSize);
legend(hp,{'Intersected faces','Normal directions','Ray/Line points','Intersection points'},'Location','SouthOutSide')
clear hp;
axisGeom(gca,fontSize); axis off;
colormap(viridis(2)); caxis([0 1]);
camlight headlight;
drawnow;

Example input variations

This example aims to show the effect of the optional input parameters

cFigure;

for testCase=1:3

    switch testCase
        case 1
            rayType='ray';
            triSide=0;
            p_origin=[0 0 2];
            p_end=[0 0 1.5];
        case 2
            rayType='ray';
            triSide=1;
            p_origin=[0 0 2];
            p_end=[0 0 1.5];
        case 3
            rayType='ray';
            triSide=-1;
            p_origin=[0 0 2];
            p_end=[0 0 1.5];
    end

    nr=p_end-p_origin; %Ray/line vector

    optionStruct.tolEps        = 1e-6;
    optionStruct.triSide   = triSide;
    optionStruct.rayType       = rayType;
    optionStruct.exclusionType = 'inclusive';
    optionStruct.paired        = 0;

    [P,indIntersect]=triSurfRayTrace(p_origin,nr,F,V,optionStruct);

    subplot(1,3,testCase); hold on;
    title([optionStruct.rayType,' / triSide: ',num2str(optionStruct.triSide)])
    gpatch(F,V,'w','k',faceAlpha,1);
    hp(1)=gpatch(F(indIntersect(:,2),:),V,'kw','k',1,1);
    hp(2)=patchNormPlot(F,V,[],'f','g');
    hp(3)=quiverVec(p_origin,nr,[],'b');
    hp(4)=plotV(P,'r.','MarkerSize',markerSize);
    legend(hp,{'Intersected faces','Normal directions','Ray/Line points','Intersection points'},'Location','SouthOutSide')

    clear hp;
    axisGeom(gca,fontSize); axis off;
    colormap(viridis(2)); caxis([0 1]);
    camlight headlight;

end
drawnow;

cFigure;

for testCase=1:5

    switch testCase
        case 1
            rayType='line';
            triSide=0;
            p_origin=[0 0 2];
            p_end=[0 0 1.5];
        case 2
            rayType='line';
            triSide=0;
            p_origin=[0 0 2];
            p_end=[0 0 0];
        case 3
            rayType='line';
            triSide=0;
            p_origin=[0 0 2];
            p_end=[0 0 -2];
        case 4
            rayType='line';
            triSide=1;
            p_origin=[0 0 2];
            p_end=[0 0 -2];
        case 5
            rayType='line';
            triSide=-1;
            p_origin=[0 0 2];
            p_end=[0 0 -2];
    end

    nr=p_end-p_origin; %Ray/line vector

    optionStruct.tolEps        = 1e-6;
    optionStruct.triSide       = triSide;
    optionStruct.rayType       = rayType;
    optionStruct.exclusionType = 'inclusive';
    optionStruct.paired        = 0;

    [P,indIntersect]=triSurfRayTrace(p_origin,nr,F,V,optionStruct);

    subplot(2,3,testCase); hold on;
    title([optionStruct.rayType,' / triSide: ',num2str(optionStruct.triSide)])
    gpatch(F,V,'w','k',faceAlpha,1);

    if ~isempty(P)
        hp(1)=gpatch(F(indIntersect(:,2),:),V,'kw','k',1,1);
        hp(2)=patchNormPlot(F,V,[],'f','g');
        hp(3)=plotV([p_origin; p_end],'b.-','MarkerSize',markerSize,'LineWidth',3);
        hp(4)=plotV(P,'r.','MarkerSize',markerSize);
        legend(hp,{'Intersected faces','Normal directions','Ray/Line points','Intersection points'},'Location','SouthOutSide')
    else
        hp(1)=patchNormPlot(F,V,[],'f','g');
        hp(2)=plotV([p_origin; p_end],'b.-','MarkerSize',markerSize,'LineWidth',3);
        legend(hp,{'Normal directions','Ray/Line points'},'Location','SouthOutSide')
    end

    text(p_origin(1),p_origin(2),p_origin(3),'  Point 1: Origin','FontSize',fontSize);
    text(p_end(1),p_end(2),p_end(3),'  Point 2: End','FontSize',fontSize);
    clear hp;
    axisGeom(gca,fontSize); axis off;
    colormap(viridis(2)); caxis([0 1]);
    camlight headlight;

end
drawnow;

Example use for ray tracing of paired ray-face intersections

This example shows paired analysis. This means that exactly one ray is provided for each face and only intersections with these individual ray-face pairs are computed.

VF=patchCentre(F,V);
indSelect=find(VF(:,3)>0);

NF=patchNormal(F,V);

Nr=-NF(indSelect,:);
P_origin=VF(indSelect,:)+1.1*NF(indSelect,:);

optionStruct.tolEps        = 1e-6;
optionStruct.triSide       = 1;
optionStruct.rayType       = 'ray';
optionStruct.exclusionType = 'inclusive';
optionStruct.paired        = 1;

[P,indIntersect,d]=triSurfRayTrace(P_origin,Nr,F(indSelect,:),V,optionStruct);

cFigure; hold on;
title([optionStruct.rayType,' / triSide: ',num2str(optionStruct.triSide)])
gpatch(F,V,'w','k',0.5,1);
hp(1)=gpatch(F(indSelect(indIntersect(:,2)),:),V,'kw','k',1,1);
hp(2)=quiverVec(P_origin,Nr,[],'b');
hp(3)=plotV(P,'r.','MarkerSize',markerSize);
legend(hp,{'Intersected faces','Rays','Intersection points'},'Location','SouthOutSide')
clear hp;
axisGeom(gca,fontSize); axis off;
colormap(viridis(2)); caxis([0 1]);
camlight headlight;

Example use for ray tracing of paired line-face intersections