10 files changed, 1604 insertions, 1579 deletions
diff --git a/worksheets/README.md b/worksheets/README.md
index d56eece..fd05063 100644
--- a/worksheets/README.md
+++ b/worksheets/README.md
@@ -1 +1 @@
-This directory is for "markdown" (.md) files that you will edit for the worksheet portion of each assignment.
+This directory is for "markdown" (.md) files that you will edit for the worksheet portion of each assignment.
diff --git a/worksheets/a1_textrain.md b/worksheets/a1_textrain.md
index 6ce1142..834f2b1 100644
--- a/worksheets/a1_textrain.md
+++ b/worksheets/a1_textrain.md
@@ -1,80 +1,82 @@
-# Assignment 1 (Text Rain) Worksheet
-
-For the conceptual worksheets in this course, we'll provide a Markdown
-template from the shared-upstream repository. As described in the Canvas
-assignment handouts, you'll pull each Markdown template into your repository,
-directly edit your local copy with your answers, and commit and push your
-answers to GitHub in your `worksheets` folder of your repository. If you're
-unfamiliar with Markdown syntax, [check out this lovely guide provided by
-GitHub](https://guides.github.com/features/mastering-markdown/) before you get
-started.
-
-_Do not make a copy of the provided Markdown template and submit that instead._
-Our grading scripts will be looking for these modified files within your
-`worksheets` folder of your repository. Do not change the filenames, simply
-modify the contents.
-
-## Background
-
-By default, Processing uses the integer-based `0-255` convention to represent
-colors. For instance, bright, full-saturation red is represented as
-`color(255, 0, 0)`.  Processing also supports grayscale colors; black is
-`color(0)` and white is `color(255)`. You may wish to look at the [color class
-documentation](https://processing.org/reference/color_.html) and/or the
-[tutorial explaining color in
-Processing](https://processing.org/tutorials/color/).
-
-Here are a couple of questions to get you thinking about how to work with
-pixel arrays and colors in this format.  Note:  These are very brief questions
-in this first worksheet, so this may not take you long at all.  That's ok!
-
-
-## Q1: Indexing
-
-As mentioned in the assignment handout, accessing/setting pixel data via
-Processing's `get()` and `set()` routines is a bit easier to code, but it's
-much slower than directly accessing/changing a [PImage
-object's](https://processing.org/reference/PImage.html) `pixels[]` array.
-Processing stores a 2D image in this 1D array, so getting the proper pixel out
-requires a little additional math.
-
-In the code block below, write the equation for obtaining the index in the 1D
-array from a (row, column) in the 2D pixels array. Keep in mind you can use
-information from `inputImg` to help you.
-
-```
-PImage inputImg = loadImage("test.jpg");
-
-// your code should work for any valid values for row and column, we've 
-// randomly picked the values (2, 2) here as an exmaple.
-int row = 2;
-int column = 2;
-
-// write your answer in terms of the row and column defined above
-int index1D = /* --- Fill this in --- */;
-```
-
-
-## Q2: Thresholding
-
-The image processing technique known as *thresholding* will be useful while
-creating your Text Rain. During the thresholding operation, if a pixel's
-grayscale value is less than `threshold`, then it becomes black. If the
-value is greater than or equal to `threshold`, it becomes white. In the example below,
-assume the image has already been converted to grayscale.  This means the
-red, green, and blue channels are all equal.  So, you can get the grayscale
-value by accessing any one of the color channels red, green, or blue.
-
-In the code block below, write a Java code snippet for thresholding one pixel
-(`inputPixel`) to black or white.
-
-```java
-final int threshold = 128;
-
-// Returns: thresholded color (black or white)
-color thresholdPixel(color inputPixel) {
-
-  /* --- Fill this in --- */
-
-}
-```
+# Assignment 1 (Text Rain) Worksheet
+
+For the conceptual worksheets in this course, we'll provide a Markdown
+template from the shared-upstream repository. As described in the Canvas
+assignment handouts, you'll pull each Markdown template into your repository,
+directly edit your local copy with your answers, and commit and push your
+answers to GitHub in your `worksheets` folder of your repository. If you're
+unfamiliar with Markdown syntax, [check out this lovely guide provided by
+GitHub](https://guides.github.com/features/mastering-markdown/) before you get
+started.
+
+_Do not make a copy of the provided Markdown template and submit that instead._
+Our grading scripts will be looking for these modified files within your
+`worksheets` folder of your repository. Do not change the filenames, simply
+modify the contents.
+
+## Background
+
+By default, Processing uses the integer-based `0-255` convention to represent
+colors. For instance, bright, full-saturation red is represented as
+`color(255, 0, 0)`.  Processing also supports grayscale colors; black is
+`color(0)` and white is `color(255)`. You may wish to look at the [color class
+documentation](https://processing.org/reference/color_.html) and/or the
+[tutorial explaining color in
+Processing](https://processing.org/tutorials/color/).
+
+Here are a couple of questions to get you thinking about how to work with
+pixel arrays and colors in this format.  Note:  These are very brief questions
+in this first worksheet, so this may not take you long at all.  That's ok!
+
+
+## Q1: Indexing
+
+As mentioned in the assignment handout, accessing/setting pixel data via
+Processing's `get()` and `set()` routines is a bit easier to code, but it's
+much slower than directly accessing/changing a [PImage
+object's](https://processing.org/reference/PImage.html) `pixels[]` array.
+Processing stores a 2D image in this 1D array, so getting the proper pixel out
+requires a little additional math.
+
+In the code block below, write the equation for obtaining the index in the 1D
+array from a (row, column) in the 2D pixels array. Keep in mind you can use
+information from `inputImg` to help you.
+
+```java
+PImage inputImg = loadImage("test.jpg");
+
+// your code should work for any valid values for row and column, we've 
+// randomly picked the values (2, 2) here as an exmaple.
+int row = 2;
+int column = 2;
+
+// write your answer in terms of the row and column defined above
+int index1D = row * inputImg.width + column;
+```
+
+
+## Q2: Thresholding
+
+The image processing technique known as *thresholding* will be useful while
+creating your Text Rain. During the thresholding operation, if a pixel's
+grayscale value is less than `threshold`, then it becomes black. If the
+value is greater than or equal to `threshold`, it becomes white. In the example below,
+assume the image has already been converted to grayscale.  This means the
+red, green, and blue channels are all equal.  So, you can get the grayscale
+value by accessing any one of the color channels red, green, or blue.
+
+In the code block below, write a Java code snippet for thresholding one pixel
+(`inputPixel`) to black or white.
+
+```java
+final int threshold = 128;
+
+// Returns: thresholded color (black or white)
+color thresholdPixel(color inputPixel) {
+  if (blue(inputPixel) < threshold) {
+    return color(0);
+  } else {
+    return color(255);
+  }
+}
+```
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
+```
diff --git a/worksheets/a3_earthquake.md b/worksheets/a3_earthquake.md
index e38902f..125df65 100644
--- a/worksheets/a3_earthquake.md
+++ b/worksheets/a3_earthquake.md
@@ -18,7 +18,7 @@ numbers `{0.0, 1.5, 2.0, 1.3}`, the normalized value would be `v_normalized =
 These two functions, part of the C++ standard library, will be useful for your
 first question: 
 
-```
+```cpp
 /* 
  *   - `std::min_element()` - return the minimum of a vector
  *   - `std::max_element()` - return the maximum of a vector
@@ -32,9 +32,19 @@ first question:
 Using the min_element() and max_element() functions, write a routine to normalize
 the values in an arbitrary vector (list) and return a new vector:
 
-```
+```cpp
 std::vector<float> normalize_list(std::vector<float> quakeList) {
   /* --- Fill in your algorithm here --- */
+    vector<float> new_vector;
+    new_vector.resize(quakeList.size());
+    float min = std::min_element(quakeList.begin(), quakeList.end());
+    float max = std::max_element(quakeList.begin(), quakeList.end());
+    float range = max - min;
+    for (int i = 0; i < quakeList.size(); i++) {
+        new_vector[i] = (quakeList[i] - min) / range;
+    }
+    return new_vector;
+
 }
 ```
 
@@ -43,18 +53,20 @@ by hand.  What would the following code print out if you were to run it?
 Note, if your math is correct, all of the values printed should be between 0.0
 and 1.0 inclusive.
 
-```
+```cpp
 std::vector<float> quakes = {0.0, 2.3, 5.1, 1.1, 7.6, 1.7};
 std::vector<float> normalized_quakes = normalize_list(quakes);
 
 for (int i = 0; i < normalized_quakes.size(); i++) {
-    std::cout << normalized_quakes[i] << " ";
+    std::cout << normalized_quakes[i] << ", ";
 }
 std::cout << std::endl;
 ```
 Output: 
-```
+```cpp
 /* --- Fill in the expected output here (e.g. "0.0, 0.5, 0.5, 1.0, 0.5, 0.12, 0.6") --- */
+"0.0, 0.30, 0.67, 0.14, 1.0, 0.22"
+"
 ```
 
 ## Q2: Constructing a mesh
@@ -72,22 +84,28 @@ Let's practice all these concepts with a simple example of a square.  Create you
 
 **Replace this image with your drawing:**
 
-![](./img/square.png)
+![](./img/square-edited.png)
 
 Now, write out the square's vertex array, using the familiar `Point3` class
 (since it's in the *xy*-plane, assume z = 0 for all points):
 
-```
+```cpp
 std::vector<Point3> squareVertexArray = {
     /* --- Fill in your `Point3`s here */
+    Point3(0.0, 0.0, 0.0),
+    Point3(1.0, 0.0, 0.0),
+    Point3(1.0, 1.0, 0.0),
+    Point3(0.0, 1.0, 0.0)
 };
 ```
 
 Finally, write out the square's index array based on the indices you defined in the picture above. Make sure your indices are defined in counter-clockwise order so that a 3D camera looking down on your square from some +Z height above will see the front faces of your triangles.
 
-```
+```cpp
 std::vector<int> squareIndexArray = {
     /* --- Fill in your first triangle indices --- */
+    0, 1, 3,
     /* --- Fill in your second triangle indices --- */
+    1, 2, 3
 };
 ```
diff --git a/worksheets/a4_dance.md b/worksheets/a4_dance.md
index fe174fe..6e0cd85 100644
--- a/worksheets/a4_dance.md
+++ b/worksheets/a4_dance.md
@@ -11,7 +11,7 @@ Here's what the house looks like when viewed from some +Z height above and looki
 ### Q1.1 Basic translation
 
 Here's a simple translation matrix.  Draw a picture of the house to show what it would look like if transformed by this matrix.
-```
+```cpp
 Matrix4 trans = Matrix4::Translation(Vector3(0.0, 0.5, 0.0));
 ```
 ![House transformed by trans](file path to your image)
@@ -19,7 +19,7 @@ Matrix4 trans = Matrix4::Translation(Vector3(0.0, 0.5, 0.0));
 ### Q1.2 Basic scaling
 
 Here's a simple scaling matrix.  Draw a picture to show what the original house would look like if transformed by this matrix.
-```
+```cpp
 Matrix4 scale = Matrix4::Scale(Vector3(2.0, 1.0, 1.0));
 ```
 ![House transformed by scale](file path to your image)
@@ -27,7 +27,7 @@ Matrix4 scale = Matrix4::Scale(Vector3(2.0, 1.0, 1.0));
 ### Q1.3 Basic rotation
 
 Here's a simple rotation matrix.  Draw a picture to show what the original house would look like if transformed by this matrix.
-```
+```cpp
 Matrix4 rot = Matrix4::RotateZ(GfxMath::toRadians(45.0));
 ```
 ![House transformed by rot](file path to your image)
@@ -36,7 +36,7 @@ Matrix4 rot = Matrix4::RotateZ(GfxMath::toRadians(45.0));
 ### Q1.4 Composition 1
 
 Now, let's take a look at different compositions of the basic matrices above.  Draw a picture to show what the original house would look like if transformed by the following matrix.
-```
+```cpp
 Matrix4 combo1 = trans * scale * rot;
 ```
 ![House transformed by combo1](file path to your image)
@@ -45,7 +45,7 @@ Matrix4 combo1 = trans * scale * rot;
 ### Q1.5 Composition 2
 
 Let's try another.  Draw a picture to show what the original house would look like if transformed by the following matrix.
-```
+```cpp
 Matrix4 combo2 = rot * scale * trans;
 ```
 ![House transformed by combo2](file path to your image)
@@ -66,7 +66,7 @@ The diagram below illustrates this concept with the simple case of a house.  It'
 
 It can be useful in these situations to define transformation matrices for moving from one coordinate space to another.  For example, given some point defined in the door's coordinate system, such as one of the vertices of the door, we could transform it into the siding's coordinate system like this:
 
-```
+```cpp
 // Transforms points in the door's coordinate system to the siding's coordinate system.
 Matrix4 doorToSiding = Matrix4::Translation(Vector3(0.5, -0.2, 0.0));
 
@@ -76,7 +76,7 @@ Point3 theSamePtExpressedInSidingSpace = doorToSiding * ptInDoorSpace;
 ```
 
 Similarly, these matrices can convert between the other spaces we've talked about.
-```
+```cpp
 // Transforms points in the siding's coordinate system to the house's coordinate system.
 Matrix4 sidingToHouse = Matrix4::Translation(Vector3(0.0, 0.5, 0.0));
 
@@ -92,7 +92,7 @@ show the combined transformation from Door-Space into World-Space as a matrix
 multiplication, then show how to transform the point `pInDoorSpace` into
 World-Space. Lastly, show the numeric representation of `pInWorldSpace`.
 
-```
+```cpp
 // The magenta point `p` from the diagram, in Door-Space
 Point3 pInDoorSpace = Point3(0.2, 0.4, 0.0);
 
@@ -105,7 +105,7 @@ Point3 pInWorldSpace = /* --- Fill this in --- */
 
 ### Q2.2 Let's double-check your work now by calculate the actual "world space" coordinates for p.  Show what the following code would output:
 
-```
+```cpp
 std::cout << "p in World-Space: " << pInWorldSpace << std::endl;
 /* --- Fill in output for std::cout here --- */
 ```
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