Zho:Raycaster

A raycaster is a 专案 that renders a 3D world based on a 2D map. This is a working example. A raycaster in Scratch is usually single frame and low resolution, to prevent lag.

Raycasting should not be mistaken with raytracing, which renders rays with more physical accuracy, catering to reflection and refraction of light rays, and traces rays in two dimensions rather than one dimension like in a raycaster.

Concept
Raycasting works by casting "rays" to measure the distance to the nearest wall, hence the term "raycaster". The program send out rays starting from the player, moving forward until it hits a wall, at which point it takes the distance it has traveled and draws a column based on the distance. The closer the wall, the larger the column. The rays are sent in different directions, with the angle sent determining where the column will be drawn. A ray sent out to the right side of the player's viewpoint will draw a column at the right side of the screen and a ray sent to the left will draw a column at the left. After all rays have been sent, the complete picture will be seen.

Sprite Based vs List Based
There are two types of raycaster that can be programmed: the sprite-based method, and the 清单-based method. Each has their own advantages and disadvantages:

For beginners, it is recommended to start by making the sprite-based method, as it is easy and uncomplicated, but slow. More advanced programmers and those who have finished making a sprite-based raycaster, can make an array based raycaster, which is faster but more complicated.

Sprite-Based Raycaster
In this raycaster, you will need three sprites: The tutorial below will teach you how to make a working sprite-based Raycaster. Here is a finished example
 * A pixel, the "sensor"
 * This moves to the player's position, points in the direction the player is facing, then moves forwards until it touches the map
 * It then records the distance moved in a 清单.
 * It repeats this for many angles to the left and right of the direction.
 * A 480x360 rectangle with certain inner paths cleared out, the "map"
 * The rectangle left after clearing some paths is used to obstruct the sensor
 * Another pixel, the "renderer"
 * The renderer draws each wall based on the distance given by the ray

Creating the map
Make a map 角色 with walls, make sure it has a closed outside area. Then, add the following 程式 to it: 當 @greenflag 被點擊 重複無限次 筆跡清除 定位到 x: (0) y: (0) end

當 @greenflag 被點擊 定位到 x: (0) y: (0) 效果 [幻影 v] 設為 (100)

Movement
Make a movement sprite that has a one pixel by one pixel 造型. Then put it inside the walls of your map sprite. Then add this script to it: 當 @greenflag 被點擊 定位到 x: (-20) y: (0) // assuming that that is where you put your sprite 變數 [drawing v] 設為 [0] 變數 [touching wall v] 設為 [0] 效果 [幻影 v] 設為 (100) 重複無限次 如果 <<(drawing) = [1]> 不成立> 那麼 如果 <[向右 v] 鍵被按下？> 那麼 右轉 @turnright (2) 度 // this can be adjusted to rotate faster, good for fighting lag 廣播訊息 [sense v]   end 如果 <[向左 v] 鍵被按下？> 那麼 右轉 @turnright (-2) 度 // this can be adjusted to rotate faster, good for fighting lag 廣播訊息 [sense v]   end 如果 <<(touching wall) = [1]> 不成立> 那麼 如果 <[向上 v] 鍵被按下？> 那麼 移動 (speed) 點 // where speed is the desired amount of steps you want it to move 廣播訊息 [sense v]     end end 如果 <<(touching wall) = [-1]> 不成立> 那麼 如果 <[向下 v] 鍵被按下？> 那麼 移動 <(speed) * (-1)> 點 // where speed is the desired amount of steps you want it to move 廣播訊息 [sense v]     end end end end

Also, clicking the information button on this sprite and clicking "don't rotate" speeds it up a little and reduces lag.

Wall sensing
You now have your map and something that moves around in that map, but the only thing that will stop it moving is 变量 values. Add this wall sensing script to the wall sensing sprite: 當 @greenflag 被點擊 效果 [幻影 v] 設為 (100) 重複無限次 如果 <<(drawing) = [1]> 不成立> 那麼 定位到 [movement v] 位置 // where movement is the movement sprite 面朝 <[direction v] 或 [movement v]> 度 移動 (speed) 點 如果 <碰到 [walls v] ?> 那麼 變數 [touching wall v] 設為 [1] 變數 [touching wall v] 設為 [0] 移動 <(speed) * (-2)> 點 如果 <碰到 [walls v] ?> 那麼 變數 [touching walls v] 設為 [-1] 變數 [touching walls v] 設為 [0] end end // the map sprite end end

Now you can move around your map without going through walls.

Distance sensing
This is the sensing script if you only have one sensor. If you have multiple sprites for sensing, you should divide up the numbers and for each sprite make a new list. 當 @greenflag 被點擊 效果 [幻影 v] 設為 (0) 刪除第 (全部 v) 項 \( [distances v] \) 定位到 [movement v] 位置

當收到訊息 [sense v] // the broadcast from before 變數 [drawing v] 設為 [1] 刪除第 (全部 v) 項 \( [distances v] \) 變數 [distance v] 設為 [0] 變數 [angle offset v] 設為 [48] 重複 (96) 次 變數 [distance v] 設為 [60] 定位到 [movement v] 位置 面朝 <<[direction v] of [movement v]> + (angle offset)> 度 重複直到 <<碰到 [walls v] ?> 或 <(distance) = [0]>> 移動 (1) 點 變數 [distance v] 改變 (-1) end 新增項目 (distance) \( [distances v] \) 變數 [angle offset v] 改變 (-1) end 等待直到 <(length of all lists) = [96]> // if you have other sensors 廣播訊息 [draw v]

Drawing
Divide up all the lists between all of the drawing sprites you have. Here is a script if you have only one drawer and one distance sensor

當收到訊息 [draw v] 定位到 x: (-237.5) y: (180) 筆跡寬度設為 (5) // because 96*5=480 which is the width of the screen 筆跡顏色設為 (Color you want) // Pick the color you want 筆跡清除 停筆 變數 [help counting v] 設為 (清單 [distances v] 的項目數 :: list) 重複 (清單 [distances v] 的項目數 :: list) 次 筆跡亮度設為 ((item (help counting) of [distances v] :: list) * ((1) + ((2) / (3)))) y 設為 ((item (help counting) of [distances v] :: list) * (4)) 下筆 y 設為 (((item (help counting) of [distances v] :: list) * (4)) * (-1)) 停筆 變數 [help counting v] 改變 (-1) 筆跡亮度設為 (0) x 改變 (5) end 變數 [drawing v] 設為 [0] This project will be slow when you run it in Scratch, even in turbo speed. Upload and run in the Flash 播放器 in 加速模式, to run in at a decent speed. However, you can run this project at a decent speed without turbo mode by running this project without screen refresh by using the 更多积木. Here is an example.

List-Based Raycaster
A list-based raycaster relies on a map stored as a list and coordinates, such as that of the player and the ray, stored as variables. This method of raycasting is very virtual, all data is stored as numbers and there are no actual sprite costumes used. The only sprite required is a moving pen to draw the walls. Here is an example. If you want an example map, one is downloadable here.



This tutorial will teach you how to make a simple list-based raycaster. It uses custom blocks to make editing easier. Make sure to check off "run without screen refresh" box.



Setting the Variables
Here is the code used to setup the variables: 定義 Set up Variables 變數 [x 座标 v] 設為 [11] 變數 [y 座标 v] 設為 [7] 變數 [Direction X v] 設為 [-1] 變數 [Direction Y v] 設為 [0] 變數 [Plane X v] 設為 [0] 變數 [Plane Y v] 設為 [0.66] 變數 [Actual Resolution v] 設為 [1] // If you aren't using resolution, you don't need this variable. 變數 [Height v] 設為 [300] 變數 [Resolution v] 設為 [12] // Resolution is not needed, but it is recommended.

The Main Loop
This is the green flag script that starts all the other scripts. 當 @greenflag 被點擊 Set Up Variables // You have already created this block! 重複無限次 停筆 // DadOfMrLog did some tests and found that setting pen size to 1 and using the pen up block reduces lag! 筆跡寬度設為 (1) 隱藏 變數 [Actual Resolution v] 設為 (((Resolution) - (16)) * (-1)) // If you want to have resolution, you need this script. Raycast // This is the next script in the tutorial. end

The Raycasting Script
Next is the main raycasting script. This block controls most of the custom blocks. Be sure to make it a run without screen refresh block.

定義 Raycast 筆跡清除 變數 [x v] 設為 [-240] // "x" is the increment variable here. Read Keys // This is the next script in the tutorial. 重複直到 <(x) > [280]> 停筆 筆跡寬度設為 (1) 筆跡亮度設為 (0) 變數 [Camera X v] 設為 ((2) * ((x) / ((Actual Resolution) - (1)))) 變數 [Ray x 座标 v] 設為 (x 座標) 變數 [Ray y 座标 v] 設為 (y 座標) 變數 [Ray X Direction v] 設為 ((X Direction) + ((Plane X) * (Camera X))) 變數 [Ray Y Direction v] 設為 ((Direction Y) + ((Plane Y) * (Camera X))) 變數 [Map X v] 設為 ([floor v] 數值 (Ray x 座标)) 變數 [Map Y v] 設為 ([floor v] 數值 (Ray y 座标)) Calculate Walls :: custom // Explained later on. Draw Walls :: custom // Explained later on. 變數 [x v] 改變 (Actual Resolution) end

Controls
One of the custom blocks in the "raycast" script was the control block, "Read Keys." Here, we'll focus on that script.

定義 Read Keys 如果 <<(Touching Wall) = [1]> 不成立> 那麼 如果 <[向上 v] 鍵被按下？> 那麼 變數 [x 座标 v] 改變 ((X Direction) * (Move Speed)) 變數 [y 座标 v] 改變 ((Y Direction) * (Move Speed)) end end 如果 <<(Touching Wall) = [-1]> 不成立> 那麼 如果 <[向下 v] 鍵被按下？> 那麼 變數 [x 座标 v] 改變 ((X Direction) * (Move Speed)) 變數 [y 座标 v] 改變 ((Y Direction) * (Move Speed)) end end 如果 <[向右 v] 鍵被按下？> 那麼 變數 [Direction X Old v] 設為 (Direction X) 變數 [Direction X v] 設為 (((Direction X) * ([cos v] 數值 ((Rotation Speed) * (-1)))) - ((Direction Y) * ([sin v] 數值 ((Rotation Speed) * (-1))))) 變數 [Direction Y v] 設為 (((Direction X Old) * ([sin v] 數值 ((Rotation Speed) * (-1)))) + ((Direction Y) * ([cos v] 數值 ((Rotation Speed) * (-1))))) 變數 [Plane X Old v] 設為 (Plane X) 變數 [Plane X v] 設為 (((Plane X) * ([cos v] 數值 ((Rotation Speed) * (-1)))) - ((Plane Y) * ([sin v] 數值 ((Rotation Speed) * (-1))))) 變數 [Plane Y v] 設為 (((Plane X Old) * ([sin v] 數值 ((Rotation Speed) * (-1)))) + ((Plane Y) * ([cos v] 數值 ((Rotation Speed) * (-1))))) end 如果 <[向左 v] 鍵被按下？> 那麼 變數 [Direction X Old v] 設為 (Direction X) 變數 [Direction X v] 設為 (((Direction X Old) * ([cos v] 數值 ((Rotation Speed) * (1)))) - ((Direction Y) * ([sin v] 數值 ((Rotation Speed) * (1))))) 變數 [Direction Y v] 設為 (((Direction X Old) * ([sin v] 數值 ((Rotation Speed) * (1)))) + ((Direction Y) * ([cos v] 數值 ((Rotation Speed) * (1))))) 變數 [Plane X Old v] 設為 (Plane X) 變數 [Plane X v] 設為 (((Plane X) * ([cos v] 數值 ((Rotation Speed) * (1)))) - ((Plane Y) * ([sin v] 數值 ((Rotation Speed) * (1))))) 變數 [Plane Y v] 設為 (((Plane X Old) * ([sin v] 數值 ((Rotation Speed) * (1)))) + ((Plane Y) * ([cos v] 數值 ((Rotation Speed) * (1))))) end

Calculating Walls
This section explains the block that calculates the walls. Unfortunately, wall touch detection is not included. If you know how to do this, please contact Furious-.

定義 Calculate Walls 變數 [Touching Wall v] 設為 [0] 變數 [Distance X Delta v] 設為 ([sqrt v] 數值 ((1) + (((Ray Y Direction) * (Ray Y Direction)) / ((Ray X Direction) * (Ray X Direction))))) 變數 [Distance Y Delta v] 設為 ([sqrt v] 數值 ((1) + (((Ray X Direction) * (Ray X Direction)) / ((Ray Y Direction) * (Ray Y Direction))))) 變數 [Wall Found v] 設為 [0] // Once the ray hits a wall, this variable is set to one, which is the same as the boolean value "true" in this case. 如果 <(Ray X Direction) < [0]> 那麼 變數 [Step X v] 設為 [-1] 變數 [Side X Distance v] 設為 (((Ray x 座标) - (Map X)) * (Distance X Delta))

變數 [Step X v] 設為 [1] 變數 [Side X Distance v] 設為 ((((Map X) + (1)) - (Ray x 座标)) * (Distance X Delta)) end 如果 <(Ray X Direction) < [0]> 那麼 變數 [Step Y v] 設為 [-1] 變數 [Side Y Distance v] 設為 (((Ray y 座标) - (Map Y)) * (Distance Y Delta))

變數 [Step Y v] 設為 [1] 變數 [Side Y Distance v] 設為 ((((Map Y) + (1)) - (Ray y 座标)) * (Distance Y Delta)) end 重複直到 <(Wall Found) = [1]> 如果 <(Side X Distance) < (Side Y Distance)> 那麼 變數 [Side X Distance v] 改變 (Distance X Delta) 變數 [Map X v] 改變 (Step X)   變數 [side v] 設為 [0] //  The variable "side" is referring to which wall is being faced, a Y wall or an X wall. In this case, it is an X wall. 變數 [Side Y Distance v] 改變 (Distance Y Delta) 變數 [Map Y v] 改變 (Step Y)   變數 [side v] 設為 [1] //  In this case, the ray has hit a Y wall. end 變數 [Map XY v] 設為 (字串中第 (Map Y) 字\( (清單第 (Map X) 項項目\( [World Map v] \) :: list) \)) // Map XY is the item of the grid that the ray is in. Example: if X is eleven and Y is seven, then Map XY would be (letter 7 of (item 11 of World Map). 如果 <(Map XY) > [0]> 那麼     變數 [Wall Found v] 設為 [1]  end //  If Map XY is more than zero, it has hit a wall. end 如果 <(side) = [0]> 那麼   變數 [Perpendicular Wall Distance v] 設為 ([abs v] 數值 ((((Map X) - (Ray x 座标)) + (((1) - (Step X)) / (2))) / (Ray X Direction)))

變數 [Perpendicular Wall Distance v] 設為 ([abs v] 數值 ((((Map Y) - (Ray y 座标)) + (((1) - (Step Y)) / (2))) / (Ray Y Direction))) end 變數 [Line Height v] 設為 ([abs v] 數值 ((h) / (Perpendicular Wall Distance))) 變數 [Draw Start v] 設為 (((0) - (Line Height)) / (2)) 變數 [Draw End v] 設為 ((Line Height) / (2))

Drawing the Walls
The last part in this tutorial is the pen script that draws the walls. It is a very simple script.

定義 Draw Walls 筆跡顏色設為 [#179fd7] 如果 <(side) = [1]> 那麼 變數 [Brightness v] 設為 (115) // This script makes the Y walls darker than the X walls for a nice effect.

變數 [Brightness v] 設為 (150) end 定位到 x: (x 座標) y: (Draw Start) 筆跡亮度設為 ((Brightness) * (-0.2)) 筆跡寬度設為 (Actual Resolution) 下筆 定位到 x: (x 座標) y: ((2) * (Draw End)) 停筆 筆跡寬度設為 (1) 筆跡亮度設為 (0)

And that wraps up the list-based raycasting tutorial! Enjoy!