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diff --git a/worksheets/a2_carsoccer.md b/worksheets/a2_carsoccer.md index 95170c4..da09ad0 100644 --- a/worksheets/a2_carsoccer.md +++ b/worksheets/a2_carsoccer.md @@ -1,156 +1,161 @@ -# 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) --- */ -``` +# Assignment 2 (Car Soccer) Worksheet
+
+## Definitions
+
+Use the following C++ style pseudocode definitions for Q1 and Q2:
+
+```cpp
+/* 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.*
+
+```cpp
+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 = operator+(s.position, operator*(velocity,t/1000));
+//That's wrong if the velocity is per ms.
+```
+
+
+
+## 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):
+
+```cpp
+bool sphereIntersection(Sphere s1, Sphere s2) {
+ /* --- Fill in your sphere intersection code here --- */
+ Vector3 toSphere1 = abs(operator-(s1.position, s2.position));
+ //abs is the absolute value of a vector components
+ float distance = toSphere1.Length();
+ return distance < (s1.radius + s2.radius);
+}
+```
+
+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:
+
+```cpp
+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) --- */
+false
+
+print(sphereIntersection(s1, s3));
+/* --- Fill in expected output (True or False) --- */
+true
+```
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