Add more to the writeup

assignment-1/Makefile

@@ -36,7 +36,7 @@ examples/%.ppm: examples/%.txt
 examples/%.png: examples/%.ppm
 	convert $< $@
 
-writeup.pdf: writeup.md
+writeup.pdf: writeup.md $(EXAMPLES_PNG)
 	$(PANDOC) -o $@ $<
 
 clean:

assignment-1/examples/fov-demo-1.txt

@@ -0,0 +1,21 @@
+imsize 640 480
+eye 0 0 15
+viewdir 0 0 -1
+hfov 60
+updir 0 1 0
+bkgcolor 0.1 0.1 0.1
+
+mtlcolor 0 0.5 0.5
+sphere -1 -2 -5 2
+sphere 3 -5 -1 0.5
+
+mtlcolor 0.5 0.5 1
+sphere 1 2 -3 3
+sphere -6 3 -4 1
+
+mtlcolor 0.5 0 0.5
+sphere 5 5 -1 1
+sphere -6 -4 -8 7
+
+mtlcolor 0.5 1 0.5
+cylinder 5 1 -2 1 -2 1 1 2

assignment-1/examples/fov-demo-2.txt

@@ -0,0 +1,21 @@
+imsize 640 480
+eye 0 0 15
+viewdir 0 0 -1
+hfov 30
+updir 0 1 0
+bkgcolor 0.1 0.1 0.1
+
+mtlcolor 0 0.5 0.5
+sphere -1 -2 -5 2
+sphere 3 -5 -1 0.5
+
+mtlcolor 0.5 0.5 1
+sphere 1 2 -3 3
+sphere -6 3 -4 1
+
+mtlcolor 0.5 0 0.5
+sphere 5 5 -1 1
+sphere -6 -4 -8 7
+
+mtlcolor 0.5 1 0.5
+cylinder 5 1 -2 1 -2 1 1 2

assignment-1/examples/up-dir-demo-1.txt

@@ -0,0 +1,9 @@
+imsize 640 480
+eye 0 0 8
+viewdir 0 0 -1
+hfov 60
+updir 0 1 0
+bkgcolor 1 1 1
+
+mtlcolor 0.5 1 0.5
+cylinder 0 0 -4 1 0 0 1 8

assignment-1/examples/up-dir-demo-2.txt

@@ -0,0 +1,9 @@
+imsize 640 480
+eye 0 0 8
+viewdir 0 0 -1
+hfov 60
+updir 1 1 0
+bkgcolor 1 1 1
+
+mtlcolor 0.5 1 0.5
+cylinder 0 0 -4 1 0 0 1 8

assignment-1/src/scene/cylinder.rs

@@ -57,7 +57,7 @@ impl ObjectKind for Cylinder {
 
     let discriminant = b * b - 4.0 * a * c;
 
-    let mut solutions = match discriminant {
+    let possible_side_solutions = match discriminant {
       // Discriminant < 0, means the equation has no solutions.
       d if d < 0.0 => vec![],
 
@@ -76,6 +76,16 @@ impl ObjectKind for Cylinder {
       _ => unreachable!("Invalid determinant value: {discriminant}"),
     };
 
+    // Filter out solutions that don't have a valid Z position.
+    let side_solutions = possible_side_solutions.into_iter().filter(|t| {
+      let ray_point = ray.eval(*t);
+      let rotated_ray_point = rotation_matrix * ray_point;
+      let z = rotated_ray_point.z - rotated_cylinder_center.z;
+
+      // Check to see if z is between -len/2 and len/2
+      z.abs() < self.length / 2.0
+    });
+
     // We also need to add solutions for the two ends of the cylinder, which
     // uses a similar method except backwards: check intersection points
     // with the correct z-plane and then see if the points are within the
@@ -96,26 +106,19 @@ impl ObjectKind for Cylinder {
         (o.z + c.z - self.length / 2.0) / r.z,
       ]
     };
+
     // Filter out all the solutions where the z does not lie in the circle
-    solutions.extend(possible_z_intersections.into_iter().filter(|t| {
+    let end_solutions = possible_z_intersections.into_iter().filter(|t| {
       let ray_point = ray.eval(*t);
       ray_point.x.powi(2) + ray_point.y.powi(2) <= self.radius.powi(2)
-    }));
+    });
 
-    // Filter out solutions that don't have a valid Z position.
-    let solutions = solutions
-      .into_iter()
-      .filter(|t| {
-        let ray_point = ray.eval(*t);
-        let rotated_ray_point = rotation_matrix * ray_point;
-        let z = rotated_ray_point.z - rotated_cylinder_center.z;
-
-        // Check to see if z is between -len/2 and len/2
-        z.abs() < self.length / 2.0
-      })
-      .filter_map(|t| NotNan::new(t).ok());
+    let solutions = side_solutions.into_iter().chain(end_solutions.into_iter());
 
     // Return the minimum solution
-    solutions.min().map(|t| t.into_inner())
+    solutions
+      .filter_map(|t| NotNan::new(t).ok())
+      .min()
+      .map(|t| t.into_inner())
   }
 }

assignment-1/writeup.md

@@ -5,6 +5,10 @@ output: pdf_document
 
 # Raycaster
 
+#### Michael Zhang \<zhan4854@umn.edu\>
+
+---
+
 Determining the viewing window for the raycaster for this assignment involved
 creating a "virtual" screen in world coordinates, mapping image pixels into that
 virtual screen, and then casting a ray through each pixel's world coordinate to
@@ -22,7 +26,15 @@ how many degrees the screen should take up.
 Changing the angle of the field of view would result in a wider or narrower
 screen, which when paired with the aspect ratio (width / height), would produce
 a bigger or smaller viewing screen, like the orange box in the above diagram
-shows. Simply put, FOV affects how _much_ of the frame you're able to see.
+shows. Simply put, FOV affects how _much_ of the frame you're able to see. An
+example is shown here:
+
+![](examples/fov-demo-1.png){width=180px}\ ![](examples/fov-demo-2.png){width=180px}
+
+The left image uses an FOV of 60, while the right image uses an FOV of 30. As
+you can see, the left side has a wider range of vision, which allows it to see
+more of the world. (both images can be found in the `examples` directory of the
+handin zip)
 
 Curiously, distance from the eye actually doesn't really affect the viewing
 screen very much. The reason is the screen is only used to determine how to
@@ -34,10 +46,16 @@ dimensions)
 
 The up-direction vector controls the rotation of the scene. Without the
 up-direction, it would not be possible to tell which rotation the screen should
-be in:
+be in.
 
 ![Rotation determined by up direction](doc/rot.jpg){width=240px}
 
+To see what this looks like, consider the following images, where the left side
+uses an up direction of $(0, 1, 0)$, while the right side uses $(1, 1, 0)$ (both
+images can be found in the `examples` directory of the handin zip)
+
+![](examples/up-dir-demo-1.png){width=180px}\ ![](examples/up-dir-demo-2.png){width=180px}
+
 Together, all of these parameters can uniquely determine a virtual screen
 location, that we can use to cast rays through and fill pixels. We can change
 any of these to produce an image with a more exaggerated view of the scene for
@@ -76,7 +94,8 @@ $\frac{\Delta x + \Delta y}{2}$ to the point to get that)
 
 Because of the way I implemented parallel projection, it's recommended to
 either put the eye much farther back, or use `--distance` to force a much bigger
-distance from the eye for the raycaster. This is due to the size of the image.
+distance from the eye for the raycaster. See the `--help` to see how this option
+is used.
 
 ### Cylinder Intersection Notes
 
@@ -84,9 +103,30 @@ First, we will transform the current point into the vector space of the
 cylinder, so that the cylinder location is $(0, 0, 0)$ and the direction vector
 is normalized into $(0, 0, 1)$.
 
-Then it's a matter of determining if the $x$ and $y$ coordinates fall into the
-space constrained by the equation $(ox + t\times rx - cx)^2 + (oy + t\times ty -
-cy)^2 = r^2$ and if $z \le L$.
+This can be done by using a rotation matrix (since we are sure this
+transformation is just a rotation). This rotation is actually a 2D rotation,
+around the normal between the cylinder direction and $(0, 0, 1)$. We then
+rotate everything we are working with (the cylinder and the ray) into this
+coordinate system to make calculations easier.
 
-See the comments in the code for a more detailed explanation of the equation
-used.
+Then it's a matter of determining if the $x$ and $y$ coordinates fall into the
+space constrained by the equation $(o_x + t\times r_x - c_x)^2 + (o_y + t\times
+r_y - c_y)^2 = r^2$ and if $z \le L$. I can solve this using the quadratic
+formula the same way as the sphere case.
+
+We want a quadratic equation of the form $At^2 + Bt + C = 0$. The values for
+$A$, $B$, and $C$ are:
+
+- $A = r_x^2 + r_y^2$
+- $B = 2(r_x(o_x - c_x) + r_y(o_y - c_y))$
+- $C = (c_x - o_x)^2 + (c_y - o_y)^2 - r^2$
+
+Solving this for $t$ yields 0-2 solutions depending on if the equation was
+satisfied or not. Then, we can plug any solutions we get back into the ray
+equation and determine if the $z$-coordinate is in the range of the cylinder
+that we want.
+
+We will also have to do this for the ends of the cylinder, but just backwards.
+So we would start with the $z$-coordinate, solve for $t$s where the ray hits
+that $z$-plane, and then check the $x$ and $y$ values to see if they satisfy the
+ray equation as well.