From 099f3e672c88099d62db50e87590151a7ab6dc17 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Petar=20Kapri=C5=A1?= <petar.kapris@dmi.uns.ac.rs>
Date: Wed, 23 Nov 2022 15:56:49 +0100
Subject: [PATCH] Modify HitBall (quadratic equation based solution)

---
 .idea/vcs.xml                                 |  6 ++
 .../gfxlab/graphics3d/solids/Ball.java        | 68 ++++++++++---------
 2 files changed, 42 insertions(+), 32 deletions(-)
 create mode 100644 .idea/vcs.xml

diff --git a/.idea/vcs.xml b/.idea/vcs.xml
new file mode 100644
index 0000000..94a25f7
--- /dev/null
+++ b/.idea/vcs.xml
@@ -0,0 +1,6 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="VcsDirectoryMappings">
+    <mapping directory="$PROJECT_DIR$" vcs="Git" />
+  </component>
+</project>
\ No newline at end of file
diff --git a/src/xyz/marsavic/gfxlab/graphics3d/solids/Ball.java b/src/xyz/marsavic/gfxlab/graphics3d/solids/Ball.java
index 789588b..89f1bf4 100644
--- a/src/xyz/marsavic/gfxlab/graphics3d/solids/Ball.java
+++ b/src/xyz/marsavic/gfxlab/graphics3d/solids/Ball.java
@@ -1,79 +1,83 @@
 package xyz.marsavic.gfxlab.graphics3d.solids;
 
-import xyz.marsavic.geometry.Vector;
 import xyz.marsavic.gfxlab.Vec3;
 import xyz.marsavic.gfxlab.graphics3d.Hit;
 import xyz.marsavic.gfxlab.graphics3d.Ray;
 import xyz.marsavic.gfxlab.graphics3d.Solid;
-import xyz.marsavic.utils.Numeric;
 
 
 public class Ball implements Solid {
-	
+
 	private final Vec3 c;
 	private final double r;
-	
+
 	// transient
 	private final double rSqr;
 
-	
-	
+
 	private Ball(Vec3 c, double r) {
 		this.c = c;
 		this.r = r;
 		rSqr = r * r;
 	}
-	
-	
+
+
 	public static Ball cr(Vec3 c, double r) {
 		return new Ball(c, r);
 	}
-	
-	
+
+
 	public Vec3 c() {
 		return c;
 	}
-	
-	
+
+
 	public double r() {
 		return r;
 	}
-	
-	
-	
+
+
+
 	@Override
 	public HitBall firstHit(Ray ray, double afterTime) {
-		Vec3 e = c().sub(ray.p());                                // Vector from the ray origin to the ball center
-		
-		double dSqr = ray.d().lengthSquared();
-		double l = e.dot(ray.d()) / dSqr;
-		double mSqr = l * l - (e.lengthSquared() - rSqr) / dSqr;
-		
-		if (mSqr > 0) {
-			double m = Math.sqrt(mSqr);
-			if (l - m > afterTime) return new HitBall(ray, l - m);
-			if (l + m > afterTime) return new HitBall(ray, l + m);
+		// U nasoj jednacini At^2 + Bt + C = 0, gde je t vreme kada zrak pogadja dve tacke sfere
+		// diskriminanta ce nam dati da li trazeno t postoji i da li postoje 1 ili 2, ako postoje 2,
+		// iz diskriminante mozemo dobiti i njihove udaljenosti.
+		// Za sferu (x-xc)^2 + (y-yc)^2 + (z-zc)^2 = r^2 i pravu (x,y,z) = (x0,y0,z0) + t(a,b,c)
+		// (a,b,c) je ray.d(), a x0,y0,z0 je ray.p(), dok je (xc,yc,zc) centar sfere i r poluprecnik.
+		double A = ray.d().lengthSquared(), B = 2*ray.d().dot(ray.p().sub(c)), C = ray.p().sub(c).lengthSquared() - rSqr;
+		//     A = a^2+b^2+c^2,             B = 2(a(x0-xc)+b(y0-yc)+c(z0-zc)), C = (x0-xc)^2+(y0-yc)^2+(z0-zc)^2-r^2
+		double D = B*B - 4*A*C;
+		if (D > 0) {
+			double rootD = Math.sqrt(D);
+			// t = (-B+-sqrt(D))/2A
+			double tSmall = (-B-rootD)/(2*A);
+			if (afterTime < tSmall)
+				return new HitBall(ray, tSmall);
+			double tBig = (-B+rootD)/(2*A);
+			if (afterTime < tBig)
+				return new HitBall(ray, tBig);
 		}
 		return null;
 	}
-	
-	
+
+
 	class HitBall extends Hit.RayT {
-		
+
 		protected HitBall(Ray ray, double t) {
 			super(ray, t);
 		}
-		
+
 		@Override
 		public Vec3 n() {
 			return ray().at(t()).sub(c());
 		}
-		
+
 		@Override
 		public Vec3 n_() {
 			return n().div(r);
 		}
-		
+
 	}
-	
+
 }