Simple Ray Casting with ClojureScript
programming clojure ~40 minutes read

Ray casting is quite old technique, that was heavily used in the early days of game development in a lot of games to create illusion of 3D space. Most known example, and perhaps first widely successful game that used this technique, was Wolfenstein 3D, made by ID Software in 1992. There were a lot of other games for all kind of platforms, that used ray casting, for example, I remember playing labyrinth game on Siemens C35 in around 2001.

There’s probably no reason to use ray casting for rendering pseudo 3D environments today, since this technique is very limited, and modern hardware is heavily optimized for working with triangles, which allows us to create very complex geometry that is impossible to model with ray casting. But I think that ray casting is kinda cool idea, a simple concept, and definitively was a very smart move in the nineties game development. Additionally, ray casting has a lot more use cases than simple rendering engine. Also, raycasting seems not to be a real word, but I’m going to refer to this technique like that further on, because it is convenient, and engine itself can be referred to as raycaster.

For this project I’ve chosen ClojureScript because I want to get into it, and into Clojure as well. Although, my experience with Lisps is not very rich, the main usage right now is for writing functions in Emacs Lisp, but those are rather basic. I’m also going through SICP with GNU Guile and Racket, and though exercises in this book are sometimes brutal, this is not real programming experience. So the real goal of this post is rather not to implement a basic raycaster, but learn some Clojure. What, you thought we’re here for games? Just kidding, we’ll make a simple maze game too, which will be playable on this page.

But first, let’s understand what raycasting is, by going through some basic examples.

Ray casting basics

General idea behind this technique is that we can imitate 3D environment based only on 2D information. This is done by casting rays from the point, where camera stands, and measuring the length of each ray until it hits any of the line segments, that represent walls on 2D plane. I’ve prepared some pictures to illustrate this idea:

We can look at this as a top down view of our scene. But how would we convert it to a first person pseudo 3D view? The answer, as you might expect, is rays. Our camera will shoot a certain amount of rays in front of it, and we will see which rays have intersection points with our red and green walls. Let’s shoot 6 rays:

Now we can find intersections with our walls. I’ve cut those rays, and calculated their lengths - this is the only information we need to make this 2D plane into pseudo 3D scene. Going from left to right, lengths are roughly 23.7, 24.2, inf, 34.8, 30.3, 27.5 pixels each:

So, in order to make a 3D scene out of these lengths we, first, have to create an empty scene. Let’s make it 256 by 224 pixels. We then divide this scene’s width by amount of rays, to compute the width of each ray, and fill this scene with rectangles of this width, which gives us roughly 42.7 pixels wide rectangles:

This doesn’t look like 3D yet, and you can notice that there are only 5 out of total 6 rectangles presented. This is due to the fact that one ray had infinity length, since id did not intersect with anything, so we don’t draw anything there. And to make it look 3D we need to change the height of each rectangle accordingly to the length of each ray. General rule – the shorter the ray, the bigger the height:

Now this looks more like a 3D scene, isn’t it? But the walls aren’t exactly look like walls, more like a set of rectangles. We can fix this by increasing our resolution, which we do by casting more rays. Also let’s add background and remove rectangle outlines:

We can also change field of view, by keeping same amount of rays but changing the angle between those:

Which is more convincing, but still not as smooth as it could be. But, we can think about rays as about our resolution, so if we would cast 256 rays, one ray for each pixel of image width, we would get something like this:

More advanced raycasting engines can produce various perspective corrections for such rectangles, making things appear at different heights. This is often used to imitate camera shake while walking. Textures can be mapped to walls and floor, and a very basic lightning can be achieved by changing texture brightness depending on distance. Even more advanced engines allow changing vertical angle of the camera to imitate looking up and down. But we will implement pretty basic untextured raycasting, extending it further can be interesting task, but I don’t fell like doing it with canvas. Maybe later, with WebGL.

Project structure

I’ll be using shadow-cljs to manage my project. I’ve found this one very straightforward and simple to setup with Leiningen. To create cljs project via lein type this in command line (I’m using Linux, so) some details on project setup may vary for different operating systems:

$ lein new shadow-cljs raycasting

As a result it should create following file structure for us:

raycasting/
├── package.json
├── public
│   ├── css
│   │   └── style.css
│   └── index.html
├── README.md
├── shadow-cljs.edn
└── src
    └── raycasting
        └── core.cljs

Let’s look at shadow-cljs.edn:

;; shadow-cljs configuration
{:source-paths ["src"]
 :dependencies [[binaryage/devtools "0.9.7"]
                [reagent "0.8.0-alpha2"]]
 ;; set an nrepl port for connection to a REPL.
 :nrepl {:port 8777}
 :builds {:app {:target :browser
                :output-dir "public/js/compiled"
                :asset-path "/js/compiled"
                :modules {:main {:entries [raycasting.core]}}
                :devtools
                ;; before live-reloading any code call this function
                {:before-load raycasting.core/stop
                 ;; after live-reloading finishes call this function
                 :after-load raycasting.core/start
                 ;; serve the public directory over http at port 8700
                 :http-root    "public"
                 :http-port    8700
                 :preloads     [devtools.preload]}}}}

Probably you won’t need to change much here, but I’ve removed reagent dependency, because I don’t need it, so my shadow-cljs.edn looks like this:

{:source-paths ["src"]
 :dependencies [[binaryage/devtools "0.9.7"]]
 :nrepl {:port 8777}
 :builds
 {:app {:target :browser
        :output-dir "public/js/compiled"
        :asset-path "/js/compiled"
        :compiler-options {:optimizations :advanced}
        :modules {:main
                  {:entries [raycasting.core]}}
        :devtools {:http-root "public"
                   :http-port 8700
                   :preloads  [devtools.preload]}}}}

I’ve also added :compiler-options {:optimizations :advanced} to produce smaller js file, and removed :before-load and :after-load functions, because I don’t think we need those, and script initialization on page load is sufficient enough.

One last thing - we need a test page to see results of our code, so let’s create public/index.html file, where we will add our canvas, and other elements as we go.

With project setup and ready we now can begin working on ray casting by creating a camera.

Creating a camera

Since we’re going to cast rays out from the camera, we need a camera in the first place. Camera will be represented as a single point on the plane with x and y coordinates, and degree parameter. Let’s create a file src/raycasting/camera.cljs and define camera by using atom so we could later update it:

(ns raycasting.camera)

(def camera (atom {:x 0.0 :y 0.0 :degree 0.0}))
Code Snippet 1: Contents of src/raycasting/camera.cljs

Our camera is a hash map with three key-value pairs for each of its parameters. We can later access these parameters by calling keys on this map like this:

raycasting.camera> (:degree @camera)
0.0

This is quite handy, and we can update our map with assoc procedure:

raycasting.camera> (assoc @camera :degree 45.0)
{:x 0.0 :y 0.0 :degree 45.0}

Or use merge-with procedure to change value currently stored in the map, by using a some procedure, which is + in our case:

raycasting.camera> (merge-with + @camera {:degree 90.0})
{:x 0.0 :y 0.0 :degree 90.0}

You can notice that while I’ve used assoc to change my :degree to 45.0 and then used merge-with with + to add 90.0 degrees to current :degree, I’ve still got 90.0 as the result, and not the expected 135.0. This is because camera is a value, and can’t really change, and instead we’re producing a new value based on old one. And since our old value never changed, it still had 0.0 as :degree. To understand how this works we need to understand what is considered a value and why. You can skip explanations of this if you want, since it mostly has nothing to do with raycasting itself, but this still may explain certain things that we will see later in the code.

In Clojure we mostly work with values, and there are no variables as presented in other languages. To make it more clear, let’s talk about what is considered a value. For example, in Rust 42 is a value, that we can assign to a variable like this:

let mut a = 42;

We’ve created a mutable variable a, and put 42 into it. We can later mutate a to hold another value:

a -= 15;

The key here is mutate - we’re not magically transforming 42 itself into 27, we’re changing the contents of a. So a is like a box which contains a value. You can’t really do anything to 42 itself – it is and always will be 42, that’s why it is a value. So when we did a -= 15, we’ve produced a new value based on the old one, and put it into a. So values never change, only variables that hold these values change what they are holding.

As an example of something that is not a value in Rust, we can look at Vector collection:

let mut b = vec![1, 2, 3];

This is a dynamic array, that holds three elements. And we can actually change this array by using different methods that it provides, like push:

b.push(4); // now collection holds these four elements [1, 2, 3, 4]

After this push, whenever we refer to b it will hold four elements. We’ve declared b as mut, but we’re not mutating b itself, but the collection that b holds - and because of that this is not a value. mut keyword only specifies that we can mutate collection. But even if we were to drop the mut keyword in both examples, e.g. let a = 42, let b = vec![1, 2, 3], we would not be able to mutate both of these, but it still would not turn [1, 2, 3] into a value, although we can treat it as a value, but underlying semantics of a collection has not changed.

(Semi-)real-world example - I give you an apple, and ask you to give me back half of it. You slice the apple, and give me back one half. This apple is not a value, because you’ve literally changed it by slicing, and now original apple is no longer available for both of us. You now hold half of the apple, and I hold another half. This is what happens when you modify vector, or any other collection.

Then I give you an apple made out of a material that once cast, can’t be destroyed, and ask you to give me half of it. You can’t slice it, or do anything to it at all, so you take very precise measures of this apple, and cast a new piece out of the same material, and give it back to me. We now have original apple, and apple slice. Then you can throw this apple to the garbage, because you can’t really do anything with it. This is what essentially happens when you do math with numbers - you can’t change 42, you can take measure (15) and produce 27 by subtraction. And this is what makes such apple to be a value.

So in Clojure, we work with such type of data, and all of Clojure collections are immutable. But the other major aspect of Clojure’s collections is persistence. The apple I’ve described isn’t really persistent, because once you’ve made new slice, nothing really tells me what it’s past state was - was it a whole apple or 3/4 of an apple? So in order to make things persistent we must provide additional information with apple, like a serial number for example. When you cast a new slice, you create a new serial number, that contains information about old serial number. This way we can look at our piece, and determine what apple was used as a reference.

Now whenever we create new copies, we encode previous serial number into current serial number, and from any point we are able to trace back to original state of the apple.

You can argue, that this can be done with an ordinary apple just as with an indestructible one, but the difference is, that ordinary apple can be changed. Imagine that you’ve made a new apple based on it, added serial number, that encodes that it was derived from original apple, and then someone bit off a piece of original apple. Then any holder of your copy of apple will try to refer to original one and will find out not what they expected. Or maybe what they expected, since apple could have been bitten before and you’ve restored original form of an apple when made it. There’s no way to tell, and preserve correct history. So even though we can enforce mutation restrictions in Rust, this does not make vector into a value.

This is kinda what Clojure does with it’s collections. But instead of using identifiers, Clojure uses path copying for sharing structure between states. So newer state refers to some point in old state. There are many different ways to maintain persistence, which are nicely described on this Wikipedia page.

A very simple example of persistent collection we can refer to is a single linked list, that grows at the front. Let’s start with list of these three items (1 2 3). This can be represented as boxes that hold values, and have pointers to what should be next value:

So 1 refers to 2, 2 refers to 3, and 3 refers to nothing, which indicates end of the list. Now we add another element to it with at the front, which produces new list (0 1 2 3):

You can see that all we did is created a box to hold 0 and told it to point on box that holds 1. The rest thing is our old list, marked with green boxes, and we did not copied anything from it. And old list did not change at all, only new node was added to it at the front, but old list knows nothing about it. So if we stored our original list somewhere, and added 0 to it, our original list was not changed.

Furthermore, if we check identity of our new list without its first element, it will be the same as in original list:

user=> (identical? '(1 2 3) '(1 2 3))
false
user=> (def a '(1 2 3))
user=> (identical? a (rest (conj a 0)))
true

First identical? test gives us false because these are two different objects, even though their values are the same. The second identical? test gives us true, because, as I’ve said, by adding new value to the list, and then removing it, we get back original list.

And all of collections in Clojure work this way, with a promise of fast change and low memory cost. Although such collections not as fast as mutable non-persistence collections, those are much more reliable, especially when it comes to concurrent programming, and reliability much more important than speed most of the time.

But in our raycasting we will have to really change camera position, so how do we do it if collections can’t be changed, and we’re using hash map tho hold camera coordinates and angle?

Moving the camera

When we’ve created camera we’ve used atom procedure to produce a reference type that can be later atomically swapped to hold another value, and swapping mechanism is concurrently safe. So, in order to update our map, all we need to do is to call swap! procedure, and pass our atom and a procedure that will update the value:

raycasting.camera> (swap! camera (fn [c] (assoc c :degree 45.0)))
{:x 0.0 :y 0.0 :degree 45.0}

Now, when we dereference camera with @, we can actually see updated value:

raycasting.camera> @camera
{:x 0.0 :y 0.0 :degree 45.0}

Using swap with anonymous procedures is kinda tedious, so instead, let’s create a set of procedures that we will use to move the camera around:

(def radian (/ Math/PI 180.0)) 

(defn move-point [[x y] degree amount] 
  (let [angle (* degree radian)]
    [(+ x (m/three-decimal (* (Math/sin angle) amount)))
     (+ y (m/three-decimal (* (Math/cos angle) amount)))]))

(defn move-forward
  "Move `camera` forward given `amount` respecting the `degree`."
  ([camera] (move-forward camera 1))
  ([camera amount]
   (let [{x :x
          y :y
          degree :degree} camera 
         [x y] (move-point [x y] degree amount)]
     (assoc camera :x x :y y))))

This procedure will move our camera forward relatively to where camera is pointed at. We compute ➊ only once, to later convert degrees to radians by multiplication. The move-point ➋ procedure will later be used in several places of our program, so it is good to have it as a separate procedure, while move-forward is used exclusively for camera movement. And inside we have weird construction ➌ which is called Associative Destructuring. We essentially bind x, y, and degree within our let block, to the values contained in camera. Now let’s try to move our camera around:

raycasting.core> (move-forward (assoc @camera :degree 0.0) 10)
{:x 0, :y 10, :degree 0}
raycasting.core> (move-forward (assoc @camera :degree 90.0) 10)
{:x 10, :y 6.123233995736766e-16, :degree 90}

Uh oh. Moving forward with 0 degrees was fine, but when we’ve turned 90 degree, we’ve got 6.123233995736766e-16 as our y coordinate. This value is very close to 0, but we don’t really need such precision, and there are some problems with such small values in JavaScript. Let’s write a macro, that will truncate it to three decimal places, which would be more than enough for our needs:

(defmacro three-decimal
  "Truncate `double` to three decimal places."
  [num]
  `(/ (int (* 1000 ~num)) 1000.0))

(defn move-forward
  "Move `camera` forward given `amount` respecting the `degree`."
  ([camera] (move-forward camera 1))
  ([camera amount]
   (let [rad (* (:degree camera) (/ Math/PI 180.0))]
     (merge-with + camera {:x (three-decimal (* (Math/sin rad) amount))
                           :y (three-decimal (* (Math/cos rad) amount))}))))

This will not work though. The problem is, that we can’t just define macro in the same file that we’ve declared procedure. This is a difference between Clojure and ClojureScript, so we have to create new file src/raycasting/macros.cljc, and use :require-macros in our namespace definition for camera.cljs:

(ns raycasting.camera
  (:require-macros [raycasting.macros :as m]))

Now we can update move-forward to refer to macro:

(defn move-forward
    "Move `camera` forward given `amount` respecting the `degree`."
    ([camera] (move-forward camera 1))
    ([camera amount]
     (let [rad (* (:degree camera) (/ Math/PI 180.0))]
       (merge-with + camera {:x (m/three-decimal (* (Math/sin rad) amount))
                             :y (m/three-decimal (* (Math/cos rad) amount))}))))

Let’s try it:

raycasting.core> (move-forward (assoc @camera :degree 0.0) 10)
{:x 0, :y 10, :degree 0}
raycasting.core> (move-forward (assoc @camera :degree 90.0) 10)
{:x 10, :y 0, :degree 90}

Nice. Now, we can do the same thing to rotate the camera:

(defn rotate
  "Rotate `camera` by an `degree`."
  ([camera] (rotate camera 0.5))
  ([camera degree]
   (assoc camera :degree (mod (+ (:degree camera) degree) 360.0))))

And if we call this:

raycasting.core> (rotate @camera 420)
{:x 0.0, :y 0.0, :degree 60.0}

Rotate procedure ensures that our :degree stays inside 360 degrees, so when we specify turn that is more than 360 degrees, we wrap around. This are two main procedures we will later use.

Drawing

Now we can draw our camera on <canvas>. Let’s add this to our index.html:

<!DOCTYPE html>
<html lang="en-US">
  <head>
    <meta charset="UTF-8">
    <script src="js/compiled/main.js"></script>
  </head>
  <body>
    <canvas id="raycaster" width="512" height="224"></canvas>
    <script>
      window.onload = function() {
        raycasting.core.init();
      }
    </script>
  </body>
</html>

We’ve added our <canvas>, and gave it an id. We will later will be able to refer to this canvas via this id, so let’s create two vars to hold canvas object, and it’s context:

(ns raycasting.core
  (:require [raycasting.camera :as cam]))

(defonce *canvas* nil)
(defonce *ctx* nil)

(defn ^:export init []
  (when-let [canvas (. js/document getElementById "raycaster")]
    (set! *canvas* canvas)
    (when (. *canvas* -getContext)
      (set! *ctx* (. *canvas* getContext "2d")))))

We use defonce here, so when we save file, and shadow-cljs hot reloads the code, we will not redefine our *canvas* and *ctx* to nil. And init procedure will run on onload event, and set our *canvas* and *ctx*.

Let’s create draw-camera procedure, that will take current camera state, and draw it to canvas:

(defn draw-line
  ([[x1 y1] [x2 y2]]
   (draw-line [x1 y1] [x2 y2] "#000000"))
  ([[x1 y1] [x2 y2] color]
   (set! (. ctx -strokeStyle) color)
   (doto ctx
     (.beginPath)
     (.moveTo x1 y1)
     (.lineTo x2 y2)
     (.stroke))))

(defn draw-camera [camera]
  (let [[x y :as pos] [(:x camera) (:y camera)]
        pointer (cam/move-point pos (:degree camera) 7)
        width 5]
    (draw-line pos pointer "#000000")
    (set! (. ctx -fillStyle) "#000000")
    (. ctx fillRect (- x (/ width 2)) (- y (/ width 2)) width width)))

Now, if we write this to the REPL:

raycasting.core> (draw-camera @cam/camera)
nil

We should see our camera:

Now let’s add some walls to look at.

Creating walls

I need to mention, that many raycasting engines define stages in terms of squares on the grid. This is useful, because we can check intersections a lot faster, since we only need to perform checks along the ray in fixed points of space. While this is quite fast, I want arbitrary placed walls in my raycaster. Because of this our algorithm will not be as optimal, but we will be able to handle more complex wall placement.

Let’s create new file src/raycasting/stage.cljs. In this file we will define our stages. Each stage is a vector, with line segments, that have three components - beginning coordinate, endpoint, and a color. Let’s define stage, as on our example picture.

(ns raycasting.stage)

(def example-stage
  [ 
   [ 
    [23.468 126.290] 
    [106.189 87.527] 
    "#89a02c"] 
   [[124.947 40.268] [166.507 95.415] "#916f6f"] ])

So what we’re doing here is, we begin by creating a vector ➊. This vector will hold all lines that our stage uses. We define another vector ➋, that will hold beginning point ➌, ending point ➍, and wall color ➎. Lastly, we specify another line ➏, and this process can continue on and on. Bigger stages will require a lot of walls, and this can be a performance hit, but we’re not aiming for best efficiency.

Now we can implement wall drawing with our draw-line procedure, that we’ve already used in draw-camera procedure. Let’s create draw-stage procedure, that will walk through our vector of walls and draw each on the canvas:

(defn draw-stage [stage]
  (doseq [line stage]
    (apply draw-line line)))

doseq is great way to iterate on a collection for producing side effects, such as drawing on screen. Let’s move our camera to the position 119.5,180, and rotate it to 180 so it is placed as on our example. Now if we call this procedure, we should see our stage:

raycasting.core (swap! cam/camera #(assoc % :x 119.5 :y 180 :degree 180))
{:x 119.5 :y 180 :degree 180}
raycasting.core> (draw-camera cam/camera)
nil
raycasting.core> (draw-stage stage/example-stage)
nil

While we at this, notice how awkward we’ve been setting our position for camera:

(swap! cam/camera #( assoc  %  :x 119.5 :y 180 :degree 180))

#() is a shorthand for creating anonymous procedure. This procedure will call assoc ➋, and % ➌ will be our cam/camera. More elaborate way to write the same code would be (fn [camera] (assoc camera …)). We could simplify this by using reset!:

(reset! cam/camera {:x 119.5 :y 180 :degree 180})

Which is much simpler, but still very error prone, because we’ll have to remember what keys should be in map. This is not an issue for three key-value pair map, but for huge maps, it will be better to create some kind of initialization procedure. Let’s create one in raycasting.camera namespace:

(defn set-position
  "Set position of the `camera` to a certain `x`, `y`, and `dergree`.")
 ([camera] (set-position camera 0 0 0))
 ([camera x y] (set-position camera x y 0))
 ([camera x y degree] (assoc camera :x x :y y :degree (mod degree 360.0)))

This is called Multi-arity function, we’ve been using it before, but I’ve never explained what it is. In Clojure, and ClojureScript it is possible to define procedure overloading based on amount of given arguments. In this example we create three possible ways to call our procedure: ➊ - we only pass our camera parameter, and it resets it’s position to 0,0 coordinates, and set’s 0 degree angle, ➋ - we specify coordinates, but we don’t care about our angle, so we reset it, and ➌ - we provide all needed parameters, and set those accordingly with assoc. The beauty of multi-arity procedures, is that it can call itself with another amount of arguments, so in this case there’s only one real body, that does the work (➌), and others (➊, ➋) are only calling it with all needed parameters. With this procedure we can quickly set desired position for our camera:

raycasting.core> (swap! cam/camera cam/set-position) ;; reset
{:x 0 :y 0 :degree 0}
raycasting.core> (swap! cam/camera cam/set-position 10 20) ;; set coordinates
{:x 10 :y 20 :degree 0}
raycasting.core> (swap! cam/camera cam/set-position 10 20 90) ;; fully specify position
{:x 10 :y 20 :degree 90}

We can use this later, when we initialize our stages in the game.

Casting rays

Now, when we have our camera, and walls, we can finally cast some rays. Although, we’re not casting rays, but a really long line segments, because our algorithm will check for intersections between line segments of stage walls, and our rays.

First, we need some linear algebra. In particular we need to check if two line segments intersect or not. This is done by three procedures. First one checks if point lies on segment:

(defn on-segment?
  "Checks if point `[ax ay]` lies on segment defined by two points `[b
  c]`, where each point is defined as a vector `[x y]`."
  [[ax ay] [[bx by] [cx cy]]]
  (and (<= ax (max bx cx))
       (>= ax (min bx cx))
       (<= ay (max by cy))
       (<= ay (min by cy))))

This procedure accepts a point, and a line segment defined as two points, and checks whenever the point lies on that line segment. We will need this procedure, because when we will check for intersections, we need to ensure, that we’re staying inside line segments.

Next bit is orientation procedure:

(defn orientation [[ax ay] [bx by] [cx cy]]
  (let [orientation (- (* (- by ay) (- cx bx))
                       (* (- bx ax) (- cy by)))]
    (cond (> orientation 0) :cw
          (< orientation 0) :cc
          :else :colinear)))

This procedure checks the relationship of point a, and points b and c. These relationships can be :cw (for clockwise), :cc (for counter clockwise), and :colinear:

Now we can check for intersection itself:

(defn intersect?
  "Checks if two line segments intersect. Line segments are defined as
  vector of two points `[a1 a2]`, and each point is a vector of two
  coordinates `[x y]`."
  [[a1 a2] [b1 b2]]
  (let [o1 (orientation a1 a2 b1)
        o2 (orientation a1 a2 b2)
        o3 (orientation b1 b2 a1)
        o4 (orientation b1 b2 a2)]
    (or
     (and (not (= o1 o2))
          (not (= o3 o4)))
     (and (= o1 :colinear)
          (on-segment? b1 [a1 a2]))
     (and (= o2 :colinear)
          (on-segment? b2 [a1 a2]))
     (and (= o3 :colinear)
          (on-segment? a1 [b1 b2]))
     (and (= o4 :colinear)
          (on-segment? a2 [b1 b2])))))

To find the point of intersection itself, we need to calculate this two formulas:

Let’s write those as intersection procedure:

(defn intersection [[[x1 y1] [x2 y2] :as ray] [[x3 y3] [x4 y4] :as wall]]
  (let [x (/ (- (* (- (* x1 y2) (* y1 x2)) (- x3 x4)) (* (- x1 x2) (- (* x3 y4) (* y3 x4))))
             (- (* (- x1 x2) (- y3 y4)) (* (- y1 y2) (- x3 x4))))
        y (/ (- (* (- (* x1 y2) (* y1 x2)) (- y3 y4)) (* (- y1 y2) (- (* x3 y4) (* y3 x4))))
             (- (* (- x1 x2) (- y3 y4)) (* (- y1 y2) (- x3 x4))))]
    [x y]))

I’ve added :as ray and :as wall to make it more clear what these points are related to. Order doesn’t really matter, since we’re computing point, but I think it gives a slight idea of what this procedure expects.

As a final piece, we need a procedure, that will find all intersections for our ray, and return those in some form, that will be usable for us later. I’ve created this procedure, that takes our stage, and two points as ray:

(defn find-intersections [stage [origin end :as ray]]
 (->> stage
       (map (fn [wall]
              (if (intersect? ray wall)
                (let [new (intersection ray wall)]
                  [(distance origin new) new])
                [10000000 end])))
       (into {})))

Here we’re using thread last macro ➊, that essentially takes result of our expression, and puts it to the last position in next expression. We then map with an anonymous procedure, that takes wall, from our stage, and checks if it intersects? with our ray. If it does, we calculate new intersection point, and return vector of the distance between ray origin and intersection point, and this new point. When map finishes, it produces this kind of list ([10 [0 15]] [11 [4.2 22.8]] … [length [x y]]). We then convert it into a hash map, where length will be our key, and set of coordinates will be our value. The distance procedure is defined as follows:

(defn distance [[x1 y1] [x2 y2]]
  (m/three-decimal
   (Math/sqrt (+ (Math/pow (- x1 x2) 2)
                 (Math/pow (- y1 y2) 2)))))

Now we finally can cast our rays. First let’s cast set of rays and draw those without truncation at the intersection point:

(defn cast-rays [camera]
  (let [ray-count 16
        step (/ fov ray-count)
        ray-start [(:x camera) (:y camera)]]
    (loop [n (dec ray-count)
           degree (:degree (cam/rotate camera (- (/ fov 2.0))))]
      (when (>= n 0)
        (let [ray-end (cam/move-point ray-start degree 5000)]
          (draw-line ray-start ray-end "#ffe680")
          (recur (dec n)
                 (+ degree step)))))))

Now if we call our procedures for drawing rays, camera, and stage like this:

raycasting.core> (draw-stage stages/example-stage)
nil
raycasting.core> (cast-rays @cam/camera)
nil
raycasting.core> (draw-camera @cam/camera)
nil

We should see this result:

Now let’s change this procedure, so it will find ray ends before drawing:

(defn cast-rays [camera stage]
  (let [step (/ fov rayCount)
        ray-start [(:x camera) (:y camera)]]
    (loop [n (dec rayCount)
           degree (:degree (cam/rotate camera (- (/ fov 2.0))))]
      (when (>= n 0)
        (let [ray-end (cam/move-point ray-start degree 5000)]
             intersections (find-intersections stage [ray-start ray-end])
             shortest-ray (apply min (keys intersections))
             ray-end (intersections shortest-ray)
          (draw-line ray-start ray-end "#ffe680")
          (recur (dec n)
                 (+ degree step)))))))

First, we compute map of intersections ➊, then find shortest intersection length from the map by applying min procedure to list of keys in the map ➋, and lastly get closest endpoint for given ray ➌.

This way we can find all intersections of given ray with all walls, but we will draw only the shortest one, like this:

To illustrate this a bit better, let’s create simple animation by making our camera rotate:

Now we can use cast-rays procedure to make our pseudo 3D image.

Making 3D view of our scene

We’ll need to modify our cast-rays procedure, so it would return a list of rays instead of drawing it:

 (defn angle-between [[[x1 y1] [x2 y2]] [[x3 y3] [x4 y4]]]
     (let [theta1 (Math/atan2 (- y1 y2) (- x1 x2))
           theta2 (Math/atan2 (- y3 y4) (- x3 x4))
           diff (Math/abs (- theta1 theta2))]
       (min diff (Math/abs (- 180 diff)))))

(defn cast-rays [camera stage]
  (let [step (/ fov rayCount)
        ray-start [(:x camera) (:y camera)]]
       central-ray [ray-start (cam/move-point ray-start (:degree camera) 100)]
    (loop [n (dec rayCount)
           degree (:degree (cam/rotate camera (- (/ fov 2.0))))
           rays ()]
      (if (>= n 0)
        (let [ray-end (cam/move-point ray-start degree 5000)
              intersections (find-intersections stage [ray-start ray-end])
              shortest-ray (apply min (keys intersections))
              ray-end (intersections shortest-ray)]
             ray-angle (angle-between [ray-start ray-end] central-ray)
          (recur (dec n)
                 (+ degree step)
                (conj rays [ray-end shortest-ray ray-angle n]))))
       rays)))

(defn draw-rays [camera rays]
  (let [pos [(:x camera) (:y camera)]]
    (doseq [[ray] rays]
      (draw-line pos ray "#ffe680"))))

First, we’ve defined an angle-between ➊ procedure, which takes two line segments and computes angle between those in radians. We than added one extra computation before we cast rays - we compute central-ray ➋, a direction where camera is looking to. Then, we compute angle between current ray we’re casting, and central ray ➌. After that we’re conjing ➍ vector with endpoint, shortest length, angle, and ray number to a list of rays. Finally, we return list of rays ➎ to the caller. draw-rays will later use these rays afterwards and draw each one ray by ray.

Now, whenever we call this procedure, we get all useful information that we will later need to produce image. First, let’s create another procedure, that will render all our elements on screen in a sequence:

(defn render []
  (let [height (. *canvas* -height)
        width (. *canvas* -width)
        camera @cam/camera
        rays (cast-rays camera stage)]
    (. *ctx* clearRect 0 0 width height)
    (draw-rays rays)
    (draw-camera camera)
    (draw-stage stage)))
 (. js/window requestAnimationFrame render)

This is a skeleton, not a fully realized procedure. Note that at ➊, we request another frame to be drawn on our canvas. So this is more like a game loop, though not quite. We will use it as our game loop though.

So, what we do there, is we create a set of bindings on each frame, and we dereference our cam/camera to get it’s position and angle, and then cast rays from the camera on our stage. Later we clear canvas and call draw-rays, draw-camera, and draw-stage.

Calling this procedure should initiate animation sequence, so if we add (swap! cam/camera cam/rotate 1), at some point we will have animation of rotating camera. Now let’s create 3D view:

(defn draw-3d-stage [rays]
  (let [ray-width (/ (/ (. canvas -width) 2) rayCount)
        height (. canvas -height)
        canvas-width (/ (. canvas -width) 2)])

   (set! (. ctx -fillStyle) "#333")
    (. ctx fillRect canvas-width 0 canvas-width (/ height 2))
    (set! (. ctx -fillStyle) "#666")
    (. ctx fillRect canvas-width (/ height 2) canvas-width (/ height 2))

   (loop [rays rays]
      (when (not (empty? rays))
        (let [[_ distance ray-degree n] (first rays)]
             wall-height (- height distance)
              wall-height (if (< wall-height 0)
                            0
                            wall-height)
             wall-color wall-height
          (set! (. ctx -fillStyle) (str "rgb("wall-color","wall-color","wall-color")")))
         (. ctx
             fillRect
             (+ canvas-width (* n ray-width))
             (- (/ height 2) (/ wall-height 2))
             (+ ray-width 1) ;; extra pixel for border
             wall-height)
        (recur (rest rays)))))

This procedure first fills background ➊, then, we loop through each ray, we calculate wall height by simply subtracting canvas height and distance to the wall ➌, and since our canvas is 256 pixels high, we use this value as our color as well ➍. Not really pretty solution, but will do for now. Then we fill rectangle of this height, and width, with offset of half of the canvas width plus number of the ray times its width. Calling this procedure in our render procedure gives us such view:

Sure this gives us the desired 3d view, but something is not right. When we look at our walls you can see that we get some kind of fish eye effect, which we can see in full form if we look directly at the wall:

There’s a good reason for this, which we can fix, although it requires a bit of additional calculations.

Fisheye compensation

The reason for this effect is the method we’re using to calculate wall heights. Here’s how we currently view our would:

This curve is our screen, so if we were to display this on a non-flat screen with opposite curve, our image would look natural. However our screens are flat, so we need to compensate this. In order to do this we need to compute distances while taking into account the amount of degrees between camera direction and the ray we currently casting.

First, let’s declare angle-between procedure, that will return angle between two line segments, one of which will be direction where camera is facing, and the other one is ray we currently casting:

(defn angle-between [[[x1 y1] [x2 y2]] [[x3 y3] [x4 y4]]]
  (let [theta1 (Math/atan2 (- y1 y2) (- x1 x2))
        theta2 (Math/atan2 (- y3 y4) (- x3 x4))
        diff (Math/abs (- theta1 theta2))]
    (min diff (Math/abs (- 180 diff)))))

Now we can use it in our cast-rays procedure:

(defn cast-rays [camera stage]
  (let [step (/ *fov* *ray-count*)
        ray-start [(:x camera) (:y camera)]
        central-ray [ray-start (cam/move-point ray-start (:degree camera) 100)]]
    (loop [n (dec *ray-count*)
           degree (:degree (cam/rotate camera (- (/ *fov* 2.0))))
           rays ()]
      (if (>= n 0)
        (do (let [ray-end (cam/move-point ray-start degree 5000)
                  intersections (find-intersections stage [ray-start ray-end])
                  shortest-ray (apply min (keys intersections))
                  ray-end (intersections shortest-ray)]
                 ray-angle (if *compensate-fisheye*
                              (angle-between [ray-start ray-end] central-ray)
                              0)
              (recur (dec n)
                     (+ degree step)
                    (conj rays [ray-end shortest-ray ray-angle n]))))
        rays))))

We store calculated angle ➊, and then add it to our ray and conj it to our rays collection. This vector already is quite big, so it would be better to use some associative collection instead. Let’s change it:

(conj rays {:end ray-end :length shortest-ray :angle ray-angle :n n})

Now, that cast-rays returns a list of hash maps, we need to update our other procedures that expected list of vectors. I’ll omit these step, as it ain’t much different from what I’ve previously described, and this post is already way longer than I’ve thought, but using hash maps will prove more usable when we will need to incorporate other information into our ray, such as color.

Now we can use angles in draw-3d-scene procedure. We’ll change our distance computation to use Math/cos procedure, to compute corrected distance:

distance (* distance (m/three-decimal (Math/cos ray-degree)))

This should give us such result:

This looks correct, when we face wall at 90 degree angle. But if we’re aligned with wall, we get this:

Which is not right. Wall is curved for some reason.


Note: To be completely honest, up to this point I did everything without using existing raycasting tutorials. But when I’ve applied, seemingly correct fisheye compensation, and it gone away only partially, I got stuck for a while. So in order to find a correct way to compensate this fisheye effect, I’ve read this one, but for some reason the formula there didn’t work for me, so I’ve altered it.


So it seems that we’re missing the projection plane. Let’s create one:

(defn projection-distance [width]
  (m/three-decimal (/ (/ *ray-count* 2) (Math/atan (* (/ *fov* 2) cam/radian)))))

It is better to compute this once, but since we can change ray count, we have to recompute this.

With this distance we can add computation in our wall-height computation process:

(defn draw-3d-stage-example9 [rays]
  (let [ray-width (/ (/ (. *canvas* -width) 2) *ray-count*)
        height (. *canvas* -height)
        canvas-width (/ (. *canvas* -width) 2)
        projection-distance (projection-distance canvas-width)]
    (set! (. *ctx* -fillStyle) "#333")
    (. *ctx* fillRect canvas-width 0 canvas-width (/ height 2))
    (set! (. *ctx* -fillStyle) "#999")
    (. *ctx* fillRect canvas-width (/ height 2) canvas-width (/ height 2))
    (loop [rays (sort (fn [{l1 :length} {l2 :length}] (> l1 l2)) rays)]
      (when-let [ray (first rays)]
        (let [{distance :length ray-degree :angle n :n} ray
              angle-step (/ *fov* *ray-count*)
              distance (if *compensate-fisheye*
                         (* distance (m/three-decimal (Math/cos ray-degree)))
                         distance)
              wall-height (* (/ (/ height *ray-count*) distance) projection-distance (/ *fov* 4))
              wall-height (if (> wall-height height)
                            height
                            wall-height)
              wall-color (+ wall-height 10)]
          (set! (. *ctx* -fillStyle) (str "rgb(" wall-color ", " wall-color "," wall-color ")"))
          (. *ctx*
             fillRect
             (+ canvas-width (* n ray-width))
             (- (/ height 2) (/ wall-height 2))
             (+ ray-width 1) ;; extra pixel for border
             wall-height))
        (recur (rest rays))))))

This looks much better in both examples:

Although walls are now appear further. I’ve tried to make up constants that will play nice to make wall occupy whole height when we near the wall, so I’ll keep it this way. I’m sure I have some misunderstanding of the algorithm, but it works, so I’m ok with that.

Handling input and focus

Now, when we have our camera working, we can make it move by pressing arrow keys. We already have needed procedures for handling camera position and rotation, so only thing we really need is input handlers, and a way to focus our canvas, so pressing arrows would not scroll the page.

There are some libraries for handling keyboard input, but I’m a purist, so we’ll implement this without dependencies. All we need is two procedures, that check if key is pressed, and that it is released. Let’s create raycasting/input.cljs:

(ns raycasting.input)

(defonce key-states (atom {}))
(defonce focus false)

We start by defining another atom for our key states. It will hold a map of keys and their states, like this {"Up" false, "Down" true}, which means that currently the Down key is pressed down. Another one is focus which we will use to determine should we handle input or not.

Let’s add these three procedures:

(defn valid-key? [key]
  (or (= key "Escape")
      (= key "Shift")
      (= key "ArrowLeft")
      (= key "ArrowUp")
      (= key "ArrowRight")
      (= key "ArrowDown")))

(defn on-key-press [event]
  (when focus
    (let [event (if event event (. js/window -event))
          key (. event -key)]
      (when (valid-key? key)
        (. event preventDefault)
        (swap! key-states assoc key true)))))

(defn on-key-release [event]
  (when focus
    (let [event (if event event (. js/window -event))
          key (. event -key)]
      (when (valid-key? key)
        (swap! key-states assoc key false)
        (. event preventDefault)))))

We’ll get our keys as strings, and check if this is one of the keys we need. If it is, and we’re focused, we swap! our key state with either true or false, so our key-states atom always holds most recent state. Now we need to assign these procedures to events:

(set! (. js/window -onkeyup) on-key-release)
(set! (. js/window -onkeydown) on-key-press)

We also have these procedures to handle focus:

(defn on-click [event]
  (set! focus true))

(defn release-focus []
  (set! focus false))

But we set these in initialization code:

(defn ^:export init []
  (set! *canvas* (. js/document getElementById "raycaster"))
  (when *canvas*
    (. *canvas* addEventListener "mousedown" input/on-click)
    (swap! cam/camera cam/set-position 10 10 45)
    (when (. *canvas* -getContext)
      (set! *ctx* (. *canvas* getContext "2d"))
      (render))))

Final step would be to poll our keys on each frame in our render procedure. For this we create another procedure, but in raycasting.core this time:

(defn move-camera [stage key-states]
  (let [{x :x y :y :as camera} @cam/camera]
    (when (key-states "Escape")
      (input/release-focus)
      (reset! input/key-states {}))

    (when (key-states "ArrowRight")
      (if (key-states "Shift")
        (let [{x' :x y' :y} (cam/strafe camera -1.5)]
          (when (not (detect-collision stage [[x y] [x' y']]))
            (swap! cam/camera cam/strafe -1)))
        (swap! cam/camera cam/rotate -1.5)))

    (when (key-states "ArrowLeft")
      (if (key-states "Shift")
        (let [{x' :x y' :y} (cam/strafe camera 1.5)]
          (when (not (detect-collision stage [[x y] [x' y']]))
            (swap! cam/camera cam/strafe 1)))
        (swap! cam/camera cam/rotate 1.5)))

    (when (key-states "ArrowUp")
      (let [{x' :x y' :y} (cam/move-forward camera 1.5)]
        (when (not (detect-collision stage [[x y] [x' y']]))
          (swap! cam/camera cam/move-forward 1.5))))

    (when (key-states "ArrowDown")
      (let [{x' :x y' :y} (cam/move-forward camera -1.5)]
        (when (not (detect-collision stage [[x y] [x' y']]))
          (swap! cam/camera cam/move-forward -1.5))))))

We then, call this procedure each frame as early as possible. You can notice that we’re calling another procedure detect-collision, it is much like our intersection finding stuff, but it calculates end position of our camera, and checks if the path intersects with any of our walls. Not very optimal, but works good.

The last thing I want to add, is a way to control amount of rays, and field of view, as well as fisheye compensation toggle. For that we’ll need these <input> tags:

<div>
  <input type="range" id="rayCountSlider"
         min="10" max="256" step="1"></input>
  <label for="rayCountSlider">Ray Count: </label>
  <output name="rayCountValue" id="rayCountOutput"></output>
</div>
<div>
  <input type="range" id="fovSlider"
         min="10" max="360" step="1"></input>
  <label for="fovSlider">Field of View: </label>
  <output name="fovSliderValue" id="fovSliderOutput"></output>
</div>
<div>
  <input type="checkbox" id="fishEyeCompensation"></input>
  <label for="fishEyeCompensation"> FishEye compensation</label><br>
</div>

And we need a way to control those. For this, let’s add these procedures:

(def max-fov 360)
(def max-compensated-fov 180)

(defn update-ray-count [event]
  (let [value (.. event -target -value)]
    (set! *ray-count* (js/parseInt value))
    (when-let [output (. js/document getElementById "rayCountOutput")]
      (set! (. output -innerHTML) value))))

(defn update-fov [event]
  (let [value (.. event -target -value)]
    (set! *fov* (js/parseInt value))
    (when-let [output (. js/document getElementById "fovSliderOutput")]
      (set! (. output -innerHTML) value))))

(defn update-fish-eye-compensation [event]
  (let [value (.. event -target -checked)]
    (set! *compensate-fisheye* value)
    (when-let [fov-slider (. js/document getElementById "fovSlider")]
      (set! (. fov-slider -max) (if value max-compensated-fov max-fov))
      (when (and value
                 (> *fov* max-compensated-fov))
        (set! *fov* max-compensated-fov)
        (set! (. fov-slider -value) max-compensated-fov)
        (when-let [fov-output (. js/document getElementById "fovSliderOutput")]
          (set! (. fov-output -innerHTML) *fov*))))))

(defn init-inputs []
  (when-let [ray-count-slider (. js/document getElementById "rayCountSlider")]
    (set! (. ray-count-slider -value) *ray-count*)
    (. ray-count-slider addEventListener "input" update-ray-count))
  (when-let [ray-count-output (. js/document getElementById "rayCountOutput")]
    (set! (. ray-count-output -innerHTML) *ray-count*))

  (when-let [fov-slider (. js/document getElementById "fovSlider")]
    (. fov-slider addEventListener "input" update-fov)
    (set! (. fov-slider -max) (if *compensate-fisheye* max-compensated-fov max-fov))
    (set! (. fov-slider -value) *fov*))
  (when-let [ray-count-output (. js/document getElementById "fovSliderOutput")]
    (set! (. ray-count-output -innerHTML) *fov*))

  (when-let [compensate (. js/document getElementById "fishEyeCompensation")]
    (. compensate addEventListener "click" update-fish-eye-compensation)
    (set! (. compensate -value) *compensate-fisheye*)))

In short, these are event handlers, which are called when we’re interacting with these inputs. We’re setting initial values as well, as the handlers in init-input procedure.

Coloring walls

Up until now we were creating gray walls, which are fine, but boring. And you could notice that we’re drawing our lines in color, so walls have color information. Let’s update our find-intersections procedure to include color information, and use it to color our walls:

(defn find-intersections [stage [origin end :as ray]]
  (->> stage
       (map (fn [[_ _ color :as wall]]
              (if (intersect? ray wall)
                (let [new (intersection ray wall)]
                  [(distance origin new) {:end new :color (or color color "#eeeeee")}])
                [10000000 {:end end :color "#000000"}])))
       (into {})))

Now, we return a map which has length as it’s key, and another map, which holds endpoint and wall color as a value. We need to update our cast-rays procedure to use this information:

(defn cast-rays [camera stage]
  (let [step (/ *fov* *ray-count*)
        ray-start [(:x camera) (:y camera)]
        central-ray [ray-start (cam/move-point ray-start (:degree camera) 100)]]
    (loop [n (dec *ray-count*)
           degree (:degree (cam/rotate camera (- (/ *fov* 2.0))))
           rays ()]
      (if (>= n 0)
        (do (let [ray-end (cam/move-point ray-start degree 5000)
                  intersections (find-intersections stage [ray-start ray-end])
                  shortest-ray (apply min (keys intersections))]
                 {ray-end :end color :color} (intersections shortest-ray)
                  ray-angle (if *compensate-fisheye*
                              (angle-between [ray-start ray-end] central-ray)
                              0)
              (recur (dec n)
                     (+ degree step)
                     (conj rays {:end ray-end :length shortest-ray :angle ray-angle :n n :color color}))))
        rays))))

We destructuring our map ➊, and then use it’s values when we conj rays. If we use this color in our draw-3d-stage procedure, we’ll finally get results similar to what I’ve showed in the very beginning:

But it would be nice if we keep the effect that more distant walls appear darker. To do that we’ll have to parse color, and dim it by some factor:

(defn dim [color amount]
  (let [dim-factor (Math/pow 1.1 (/ (inc amount) 7))
        color (int (/ color dim-factor))]
    (if (< color 25)
      25
      color)))

(defn dim-color [color distance]
  (let [red (js/parseInt (str "0x" (subs color 1 3)))
        green (js/parseInt (str "0x" (subs color 3 5)))
        blue (js/parseInt (str "0x" (subs color 5)))]
    (str "rgb("
         (dim red distance)
         ", "
         (dim green distance)
         ", "
         (dim blue distance)
         ")")))

These two procedures will dim colors encoded as six digit hex colors, or #ffffff. We use our distance as dim factor with some computations to make it look nice. Now we can use it in our draw-3d-stage procedure:

(defn draw-3d-stage [rays]
  (let [ray-width (/ (/ (. *canvas* -width) 2) *ray-count*)
        height (. *canvas* -height)
        canvas-width (/ (. *canvas* -width) 2)
        projection-distance (projection-distance canvas-width)
        gradient (. *ctx* createLinearGradient 0 0 0 height)]
    (doto gradient
      (.addColorStop 0 "#424242")
      (.addColorStop 0.5 "#111111")
      (.addColorStop 1 "#e2e2e2"))
    (set! (. *ctx* -fillStyle) gradient)
    (. *ctx* fillRect canvas-width 0 canvas-width height)
    (loop [rays (sort (fn [{l1 :length} {l2 :length}] (> l1 l2)) rays)]
      (when-let [ray (first rays)]
        (let [{distance :length ray-degree :angle n :n color :color} ray
              angle-step (/ *fov* *ray-count*)
              distance (if *compensate-fisheye*
                         (* distance (m/three-decimal (Math/cos ray-degree)))
                         distance)
              wall-height (* (/ (/ height *ray-count*) distance) projection-distance (/ *fov* 4))
              wall-height (if (> wall-height height)
                            height
                            wall-height)
              color (dim-color color distance)]
          (set! (. *ctx* -fillStyle) color)
          (. *ctx*
             fillRect
             (+ canvas-width (* n ray-width))
             (- (/ height 2) (/ wall-height 2))
             (+ ray-width 1) ;; extra pixel for border
             wall-height))
        (recur (rest rays))))))

I’ve also added a bit more nice gradient for our background color there. This will be our final version of this procedure.

Labyrinth game

Now we can create a small labyrinth game, but we need a way to determine if the goal was reached. But first, we need a stage to play on, as our current one isn’t really a good one. I’ve came up with this:

Our goal is to reach that colored corridor. To check if we’re succeeded we’ll simply check if our camera is inside the square. To check that we’ll use our raycasting facilities. The algorithm is pretty easy:

  • We cast ray from our point to the right,
  • We count with how many walls of given square we intersect with,
  • If amount of intersections is odd then we’re inside.

We can see that this works for us:

Of course there are special cases, like when point lies on either of rectangle sides, but we can’t intersect with walls, because we detect collisions, so we’ll be fine. Here’s the code:

(defn inside-rectangle [camera [[ax ay] [bx by] [cx cy] [dx dy]]]
  (let [walls [[[ax ay] [bx by]]
               [[bx by] [cx cy]]
               [[cx cy] [dx dy]]
               [[dx dy] [ax ay]]]
        {x :x y :y} camera
        {x' :x y' :y} (cam/move-forward {:x x :y y :degree 90} 1000)]
    (->> walls
         (map (fn [wall]
                (if (intersect? [[x y] [x' y']] wall) 1 0)))
         (reduce + 0)
         odd?)))

We receive four points that define our goal, and move camera 90 degrees right to some amount. Then we map intersect? procedure across our walls, returning either 1 or 0 depending on collision detection, and reduce results with +, to finally check if the result is odd? or not.

Though we need some way to extract goal from our stage, I’ll just define it as a constant because I don’t want to make stage code even more complex as it is now, and we’re not going to change stages. So when we’re reached our goal, we’ll just teleport camera back to starting point:

(defn render []
  (move-camera stage @input/key-states)
  (when (inside-rectangle @cam/camera stage/goal)
    (swap! cam/camera cam/set-position 12 195 180))
  (let [height (. *canvas* -height)
        width (. *canvas* -width)
        camera @cam/camera
        rays (cast-rays camera stage)]
    (. *ctx* clearRect 0 0 width height)
    (draw-rays camera rays)
    (draw-camera camera)
    (draw-stage stage)
    (draw-3d-stage rays)
    (. js/window requestAnimationFrame render)))

Combining all this stuff should give us this small game:


You can click on this canvas, and use Up, Down, Left, Right to move, you also can strafe to the side while holding Shift, and pressing Esc will return focus to the page so you could scroll it with arrow keys as usual.

What I’ve learned

This project was extremely fun to do in ClojureScript, and Clojure itself is quite awesome language, although those have some differences. If you’re learning Clojure, I highly recommend Clojure for the Brave and True book, and although I didn’t finished it yet, I’ve borrowed a lot of ideas from there, like using these little Unicode circles (➊) to mark stuff for further explanations. This book has a “Peg Thing” game example, which got me thinking about trying something a bit more complex and real time with Clojure, but I wasn’t sure how to draw graphics with Java stuff, so I’ve chosen ClojureScript because canvas was very easy to reach.

After implementing this, I think that while you don’t really need all these class objects like point, line, e.t.c. as long as you’re passing those in meaningful contexts, which I didn’t really do through this post, and I expect that this code will be really hard to read after some point of time. But certainly, maps provide most of what you need from class or object, and more generic than objects.

The cleaned up source code for this project can be found here if you’re interested into looking more closely. I hope you’ve enjoyed the read, and got interested in Clojure or Lisp in particular if you’re not Lisp hacker already.