A good friend of mine wanted some help with a VR project to see if a ray (controller's motion vector) is intersecting with a spherical viewport of the user. Here's a rudimentary java program to check for a vector intersecting a sphere.
User input <- Coordinates of the two points of the vector and the coordinates of the sphere center and sphere radius
Output -> Coordinates of the point(s) of intersection
Have not programmed in Java for a couple of decades so was an interesting and enriching experience as the program slowly got built out, refined and refactored (to the best of my ability). Sure it's not computationally efficient but hoping to make it an API to use within Unity at some point!
/** Copyright - Trivikram Prasad Date: May 19, 2018 All Rights Reserved */// Program to calculate the points of intersection of a vector with a Sphereimportjava.util.Scanner;// DEFINE ALL CLASSES// 3D Point classclassPoint3D{doublex,y,z;//Coordinates of a pointpublicPoint3D(doublex,doubley,doublez){this.x=x;this.y=y;this.z=z;}}// Sphere ClassclassSphere{doublecX,cY,cZ;// Coordinates of the sphere centerdoublecR;// Radius of spherepublicSphere(doublecX,doublecY,doublecZ,doublecR){this.cX=cX;this.cY=cY;this.cZ=cZ;this.cR=cR;}}// String class -- only for formatting outputclassStringPoint{StringpX,pY,pZ;// Converting coordinate values to string values for formattingpublicStringPoint(StringpX,StringpY,StringpZ){this.pX=pX;this.pY=pY;this.pZ=pZ;}}// The main class. This is where the real s**t happenspublicclasslineSphereX{publicstaticvoidmain(String[]args){doublea,b,c;// Coefficients of the quadratic equationdoublediscr;// Square of the discriminant of the quadraticdoublet1=0.0;// parameter 1doublet2=0.0;// parameter 2Scannerin=newScanner(System.in);// Read coordinates of the first point on the lineSystem.out.print("Enter x, y, z coordinates of the 1st point on the line: ");Point3Dpoint1=readLineInputCoordinates(in);// Read coordinates of the second point on the lineSystem.out.print("Enter x, y, z coordinates of the 2nd point on the line: ");Point3Dpoint2=readLineInputCoordinates(in);// Read center coordinates and radius of sphereSystem.out.print("Enter x, y, z center coordinates and RADIUS 'r' of the sphere: ");SpheresphCenter=readSphereInputCoordinates(in);in.close();//Calculate coefficients: 'a', 'b', 'c' for the equation 'ax^2 + bx + c = 0a=Math.pow(point2.x-point1.x,2)+Math.pow(point2.y-point1.y,2)+Math.pow(point2.z-point1.z,2);b=2*((point2.x-point1.x)*(point1.x-sphCenter.cX)+(point2.y-point1.y)*(point1.y-sphCenter.cY)+(point2.z-point1.z)*(point1.z-sphCenter.cZ));c=Math.pow((point1.x-sphCenter.cX),2)+Math.pow((point1.y-sphCenter.cY),2)+Math.pow((point1.z-sphCenter.cZ),2)-Math.pow(sphCenter.cR,2);discr=Math.pow(b,2)-(4*a*c);// No intersection points`if(discr<0){System.out.println("\nVector does not intersect the sphere");return;}elseif(discr==0)// Single intersection point{System.out.println("\nVector intersects the sphere at a single point:");if(a>0){t1=-b/(2*a);StringPointXPoint=findXPoint(point1,point2,t1);System.out.println("The tangent to sphere is at "+XPoint.pX+","+XPoint.pY+","+XPoint.pZ+"\n");}else{System.out.println("Not a line\n");}}else// Two intersection points{System.out.println("\nVector intersects the sphere at two points");t1=(-b-Math.sqrt(discr))/(2*a);// 1st Vector equation parametert2=(-b+Math.sqrt(discr))/(2*a);// 2nd Vector equation parameter// Find the points of intersectionStringPointXPoint1=findXPoint(point1,point2,t1);StringPointXPoint2=findXPoint(point1,point2,t2);System.out.println("1st point of vector intersection with sphere: "+XPoint1.pX+","+XPoint1.pY+","+XPoint1.pZ);System.out.println("2nd point of vector intersection with sphere: "+XPoint2.pX+","+XPoint2.pY+","+XPoint2.pZ+"\n");}System.exit(0);}// Function for user input of sphere center coordinates and radiusprivatestaticSpherereadSphereInputCoordinates(Scannerinput){doublesphere_ctr[]=newdouble[4];Sphereinput_sphere=newSphere(0,0,0,0);for(inti=0;i<4;i++){sphere_ctr[i]=input.nextDouble();}input_sphere.cX=sphere_ctr[0];input_sphere.cY=sphere_ctr[1];input_sphere.cZ=sphere_ctr[2];input_sphere.cR=sphere_ctr[3];returninput_sphere;}// Function for user inputs of point coordinatesprivatestaticPoint3DreadLineInputCoordinates(Scannerinput){doubleline_pt[]=newdouble[3];Point3Dinput_coords=newPoint3D(0,0,0);for(inti=0;i<3;i++){line_pt[i]=input.nextDouble();}input_coords.x=line_pt[0];input_coords.y=line_pt[1];input_coords.z=line_pt[2];returninput_coords;}// Function to calculate the point of intersectionprivatestaticStringPointfindXPoint(Point3Dpoint1,Point3Dpoint2,doublet){Point3DintPoint=newPoint3D(0,0,0);StringPointXStrPoint=newStringPoint("","","");// Parametric equation of the form L = P + tU// where 'L' is the intersection point, 'P' is the point on the line and// U is the unit vector (Point2 - Point1)intPoint.x=point1.x+t*(point2.x-point1.x);intPoint.y=point1.y+t*(point2.y-point1.y);intPoint.z=point1.z+t*(point2.z-point1.z);XStrPoint=formatString(intPoint);returnXStrPoint;}// Function to format the coordinates to string for display/output to consoleprivatestaticStringPointformatString(Point3DintPoint){StringPointstrPoint=newStringPoint("","","");strPoint.pX=String.format("%.2f",intPoint.x);strPoint.pY=String.format("%.2f",intPoint.y);strPoint.pZ=String.format("%.2f",intPoint.z);returnstrPoint;}}Top comments(0)
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