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+# Assignment 2 (Car Soccer) Worksheet
+
+## Definitions
+
+Use the following C++ style pseudocode definitions for Q1 and Q2:
+
+```
+/* Use this Point3 class to store x,y,z values that define a mathematical
+ * point (i.e., a position) in 3-space.
+ */
+class Point3 {
+    float x;
+    float y;
+    float z;
+};
+
+/* Use this Vector3 class to store x,y,z values that define a vector in
+ * 3-space.  Remember, mathematically, a vector is quite different than
+ * a point.  It has a direction and a magnitude but no position!
+ * For vectors it is often useful to be able to compute the length,
+ * also known as the magnitude, of the vector.
+ */
+class Vector3  {
+    float x;
+    float y;
+    float z;
+    
+    // returns the length (i.e., magnitude) of the vector
+    float Length() {
+        return sqrt(x*x + y*y + z*z);
+    }
+};
+
+
+/* In C++ and other languages we can define operators so we can use
+ * the +, -, =, *, / operations on custom classes.  Like many graphics
+ * libraries, this is what MinGfx does to make it easy to work with
+ * points and vectors in code.  For example, recall from class that
+ * if we have a point A (Coffman Union) and we add a vector (direction
+ * and magnitude) to this, we arrive at a new point B (e.g., Murphy Hall).
+ * Conceptually, a point + a vector = a new point.  Mathematically, it
+ * does not make sense to add two points, but it does make sense to 
+ * subtract two points.  The "difference" between the Murphy and Coffman 
+ * points is a vector that tells us the direction and magnitude we would
+ * need to walk from Coffman to get to Murphy.  Here's how we can write
+ * that in code using Point3, Vector3, and operators like + and -.
+ *
+ *   Point3 murphy = Point3(5, 8, 0);
+ *   Point3 coffman = Point3(4, 6, 0);
+ *   Vector3 toMurphy = murphy - coffman; 
+ *
+ *   // or, if we were given coffman and toMurphy we could find
+ *   // the point "murphy" by starting at point "coffman" and adding
+ *   // the vector "toMurphy".
+ *   Point3 murphy2 = coffman + toMurhpy; 
+ *
+ * The code that defines these opertors looks something like this:
+*/
+
+// a point + a vector = a new point
+Point3 operator+(Point3 p, Vector3 v) { 
+   return Point3(p.x + v.x, p.y + v.y, p.z + v.z); 
+}
+
+// a point - a point = a vector 
+// the dir and magnitude needed to go from point point B to point A
+Vector3 operator-(Point3 A, Point3 B) {
+    return Vector3(A.x - B.x, A.y - B.y, A.z - B.z);
+}
+
+// a vector * a scalar = a new vector with scaled magnitude
+Vector3 operator*(Vector3 v, float s) {
+    return Vector3(v.x * s, v.y * s, v.z * s);
+}
+
+
+
+/* Given all these tools, we can define additional classes for geometries
+ * that are useful in graphics.  For example, we can represent a sphere
+ * using a Point3 for the position of the center point of the sphere and
+ * a float for the sphere's radius.
+ */
+class Sphere {
+    Point3 position;
+    float radius;
+};
+```
+
+## Q1: Eulerian Integration
+
+In computer graphics and animation, there are many forms of integration that
+are used. For simple physics models like we have in Car Soccer, Eulerian
+Integration is good enough. Eulerian Integration uses velocity and position
+information from the current frame, and the elapsed time to produce a position
+for the next frame. Write pseudocode for determining the position of the sphere in the
+next frame:
+
+*Hint: think back to the motion equations from introductory physics. Or, look
+around in the assignment handout.*
+
+```
+Vector3 velocity = Vector3(1.0, 1.0, 1.0);
+float dt = 20; // milliseconds
+
+Sphere s = Sphere {
+    position: Point3(0.0, 0.0, 0.0),
+    radius: 5.0,
+};
+
+s.position = /* --- Fill in the next frame position computation here --- */
+```
+
+
+
+## Q2: Sphere Intersection
+
+In this assignment, you will need to test intersections between spheres and
+other objects. Using the information contained within each sphere class,
+write pseudocode to determine whether or not two spheres are intersecting
+(which you can use for car/ball intersections):
+
+```
+bool sphereIntersection(Sphere s1, Sphere s2) {
+    /* --- Fill in your sphere intersection code here --- */
+    
+
+}
+```
+
+To check that your intersections work, try working through the math by hand for the
+following two cases.  You can write out the math on a scrap piece of paper.   You do
+not need to include that detail in this worksheet.  But, do change the lines below where
+it says "Fill in expected output" to indicate whether True or False would be returned:
+
+```
+Sphere s1 = Sphere {
+    position: Point3(0.0, 1.0, 0.0),
+    radius: 1.0,
+};
+
+Sphere s2 = Sphere {
+    position: Point3(3.0, 0.0, 0.0),
+    radius: 1.0,
+};
+
+Sphere s3 = Sphere {
+    position: Point3(1.0, 1.0, 0.0),
+    radius: 2.0,
+};
+
+print(sphereIntersection(s1, s2));
+/* --- Fill in expected output (True or False) --- */
+
+print(sphereIntersection(s1, s3));
+/* --- Fill in expected output (True or False) --- */
+```