diff --git a/shapes/Cyl.cc b/shapes/Cyl.cc
index 5e287b6..66f23e5 100644
--- a/shapes/Cyl.cc
+++ b/shapes/Cyl.cc
@@ -16,6 +16,7 @@ Cyl::Cyl(double bottom_radius, double top_radius, double height)
     m_height = fabs(height);
     if (m_height == 0.0)
         m_height = 1.0;
+    m_slope = (m_top_radius - m_bottom_radius) / m_height; /* rise over run */
 }
 
 Shape::IntersectList Cyl::intersect(const Ray & ray)
@@ -28,9 +29,33 @@ Shape::IntersectList Cyl::intersect(const Ray & ray)
      *                 x = R0x + tRdx
      *                 y = R0y + tRdy
      *                 z = R0z + tRdz
-     * Side equation:  x^2 + y^2 = 
-     * Combined:       
+     * Side equation:  x^2 + y^2 = (m*z + b)^2
+     * Combined:       (R0x+t*Rdx)^2 + (R0y+t*Rdy)^2 = (m*(R0z+t*Rdz) + b)^2
+     * Expanded:       (R0x*R0x + (t*t)*Rdx*Rdx + 2*R0x*t*Rdx)
+     *                 + (R0y*R0y + (t*t)*Rdy*Rdy + 2*R0y*t*Rdy)
+     *                 = ((m*R0z+m*t*Rdz)^2 + b*b + 2*m*(R0z+t*Rdz)*b)
+     *                 = ((m*R0z*m*R0z + m*m*t*t*Rdz*Rdz + 2*m*R0z*m*t*Rdz)
+     *                  + b*b + 2*m*R0z*b + 2*m*t*Rdz*b)
+     * Quadratic form: (t*t)(Rdx*Rdx + Rdy*Rdy - m*m*Rdz*Rdz)
+     *                 + (t)(2*R0x*Rdx + 2*R0y*Rdy - 2*m*R0z*m*Rdz - 2*m*Rdz*b)
+     *                 + (R0x*R0x + R0y*R0y - m*m*R0z*R0z - b*b - 2*m*R0z*b)
+     *                 = 0
      */
+    double Rdx = ray_inv.getDirection()[0];
+    double Rdy = ray_inv.getDirection()[1];
+    double Rdz = ray_inv.getDirection()[2];
+    double R0x = ray_inv.getOrigin()[0];
+    double R0y = ray_inv.getOrigin()[1];
+    double R0z = ray_inv.getOrigin()[2];
+    double m = m_m;
+    double m2 = m*m;
+    QuadraticSolver solver(Rdx * Rdx + Rdy * Rdy - m2 * Rdz * Rdz,
+                           2.0 * (R0x*Rdx + R0y*Rdy - m2*R0z*Rdz - m*Rdz*m_b),
+                           R0x*R0x + R0y*R0y
+                             - m2*R0z*R0z - m_b*m_b - 2*m*R0z*m_b
+                          );
+
+    Solver::Results results = solver.solve();
 
     return res;
 }
diff --git a/shapes/Cyl.h b/shapes/Cyl.h
index ad1afcf..89f5894 100644
--- a/shapes/Cyl.h
+++ b/shapes/Cyl.h
@@ -17,6 +17,7 @@ class Cyl : public Shape
         double m_top_radius;
         double m_top_radius_2;
         double m_height;
+        double m_slope;
 };
 
 #endif