Testing the Numbers for Platformer Player Controls

Taxonomy of Virtual Spaces Part II

As detailed in my last post, I used Excel to create formulas to translate Super Mario Bros. physics values (measured in pixels and frames) into metric values (meters and seconds) so that I can use them with my character controller in Unity. It didn't take long to realize that something was wrong.

These make for VERY slow acceleration!

For the acceleration values, I multiplied the calculated distance values by 60 when I meant to multiply them by 60^2 (3600). No wonder my character seemed to get up to speed slowly: I was off by a factor of 60! Once I made that change, the character felt much snappier.

When comparing directly to SMB, my run speed seems slightly fast. In SMB, it takes Mario about 3 seconds to cross one screen width (16 blocks) from a standstill when walking and about 2 seconds when running. My character is covering that distance (16 meters) in a little less time (about 2.6 and 1.6 seconds, respectively), but it is close enough that I can move on and concern myself with other aspects of the controller.

Implementing Player Platformer Controls

Taxonomy of Virtual Spaces Part II

After determining the formulas to use to design a player avatar controller for 2-D platformer style gameplay, I need to actually create the code and determine what values to use. How fast should the avatar run? How high should they jump? How far can they jump? What about double-jumping, jump-dash, or other types of movement?

This project is focused on game spatiality, so the character controller is really just a means to an end. The controls should be intuitive, familiar, uncomplicated, and even archetypal. As a start, the obvious choice would be to emulate Super Mario Bros.

Start with Super Mario Physics

A Complete Guide to SMB's Physics Engine by Jdaster64 (link to archive.org)

How fast does Super Mario run? How high does he jump? How far does he jump? This information was collected by Jonathan Aldrich, a.k.a. Jdaster64. Aldrich has spent years meticulously compiling mathematical data about how many Nintendo games function. His A Complete Guide to SMB's Physics Engine document, linked above, gives information on how Super Mario and Luigi move in Super Mario Bros. and the Japanese version of Super Mario Bros. 2 (known in the USA as Super Mario Bros.: The Lost Levels).

I don't know about Aldrich's methodology for acquiring his data and it would be prohibitively difficult to verify every value he's posted. However, I only need a controller that feels authentic to the player, not an emulation with pixel-perfect accuracy. At a cursory examination, his numbers make sense, and I will certainly know from testing if the results are accurate.

Aldrich's distance values are measured using screen units that make sense from the structure of the NES game console. Each different unit of measure is 1/16 the size of the previous unit and each is recorded using a hexadecimal value. One "Block" is 16 pixels across (using the basic 16 x 16 tile size of the NES). One "Pixel" is about 1/240th of the height of the screen and 1/256th of the width of the screen (the NES displays this to fit in the 4:3 aspect ratio of a standard definition television, so the pixels are slightly wider than they are tall).

SMB also tracked fractions of pixels of distance, which allowed for very precise values for acceleration and speed. There are also "Subpixels" (1/16 of a pixel), "Sub-subpixels" (1/256 of a pixel), and even "Sub-sub-subpixels" (1/4096 of a pixel).

Velocity is measured as distance moved per frame, or in 1/60 of a second. Acceleration is the amount of velocity change in 1/60 of a second.

How Many Pixels per Meter?

Converting Aldrich's values to metric

Virtual spaces in the Unity engine are measure in meters, which are typically equal to our own real-world metric system. I reckon that one block should be equal to one meter. In SMB, Mario grows from about 1 block high to about 2 blocks high when becoming Super Mario. 1-meter and 2-meter are both height values within the realm of real-world human possibilities. In addition, it makes things easier to build a world environment where each block is one meter across.

I used Excel to convert blocks and pixels to meters and convert frames to seconds. Now I have the number values to set my velocities, distances, and acceleration values. Now I need a script to give everything structure.

Ultimate 2D Platformer Controller

Ultimate 2D Platformer Controller by Sasquatch B Studios

Fortunately, I found a tutorial video (linked above) for a character controller that uses Unity's new Input System (which is a learning objective for me in this project) and is built using the same formulas I wrote about in my last post. The scripts seem well designed and the results are good so far. The jump values can easily be edited and include options like coyote time and hang time. There is a fair amount of extra functionality I will still need to add (such as different jump heights for walking and running), but this seems like the perfect structure to start with.

UPDATE:

If you follow the Ultimate 2D Platformer Controller tutorial linked above, be sure to watch part 2 of the tutorial here. The first part of the video cleans up and fixes a few bugs from the original video and, if you are interested, shows how to add wall slides, wall jumps, and mid-air dashes.

Designing Platformer Player Controls

Taxonomy of Virtual Spaces Part II

One of the first steps in this project is to code a player avatar controller for 2-D platformer style gameplay, to allow the user to comfortably navigate the virtual environment. This also gives me a chance to use Unity's new Input System for the first time, as I've always used the Input Manager in previous projects.

Now, where to begin? Although I've created a few platformers in my time (like the experimental Super Mario Love (Rowe, 2019)), I've never created one professionally or for broader release. I've studied the game genre extensively and know enough to give my students advice on developing camera systems or how to adjust gravity to not feel "floaty," but this will be a new endeavor for me.

Building a Better Jump

Math for Game Programmers: Building a Better Jump (J. Kyle Pittman, 2016, GDC)

Building a Better Jump by J. Kyle Pittman is a lecture on using physics formulas to plan and design a platformer game controller, part of the "Math for Game Programmers" series of tutorials at the Game Developers Conference.

A common way to create a platformer game is to open the Unity editor, create a player character game object with a rigidbody, and write a script that applies a force on the object in an upward vector when the player presses the space bar. Then, through trial and error, the developer tunes the force value until the object can "jump" to the desired height. This tends to feel floaty, require a lot of iteration, and using Unity's default physics values tends to make it feel like every other Unity game out there.

How high?

Formulas for initial velocity and gravity

Pittman's approach is to remember your college physics formulas! By using the projectile motion vs. gravity formula f(t) = 1/2 gt^2 + v0t + p0 (Blogger is not great for writing formulas!), he shows that the initial velocity (v0)and gravity (g) values can be calculated based on how high you want the character to jump at the apex (h) and how much time you want the character to reach that apex (t). For example, if I want a character to jump 5 meters straight up and take 0.5 seconds to get there, then I should use a jump velocity of 20 m/s and a gravity value of 40 m/s^2 (or about 4 times our Earth's gravity).

How far?

Pittman uses more formulas to determine what lateral velocity (running speed) is needed to clear a certain jump distance. Remember calculating for how far a cannonball can fly before it impacts with the ground? No need to worry about launch angles here. Pittman shows how to calculate what x velocity is needed using time, height, and lateral distance requirements.

Break the Rules

Increase gravity at apex of jump to give the character a sense of weight

The formulas so far create a jump that is a perfect parabola, which unfortunately feels "floaty" and doesn't feel good to play. Here, Pittman quotes Game Feel (Swink, 2008), stating that in Super Mario Bros., the force of gravity triples at the apex of Mario's jump. (Swink: "At the apex of the jump, when velocity reaches 0, gravity is raised artificially by a factor of three, pulling Mario back to the ground with a much greater force than the one he overcame to get airborne in the first place" (2008, pg. 211). This "fast fall" technique makes the player feel "weighty" instead of "floaty." This is a simple technique that I've been teaching to my students for years.

Other modifications

Double jumping

Fast fall, double jumping, and variable-height jumps are all calculated using the same basic methods: use multiple parabolas or partial parabolas to determine the values needed. Pittman's methods give a great foundation for designing a platformer character controller from the ground up by the game's navigational requirements rather than fumbling around by trial and error.

There are still other important aspects of designing a platformer controller that are outside of scope of this lecture, such as coyote time, jump buffering, and hang time. Most of these involve setting timers and allowing the player to input a jump command when their character is not currently "grounded."

(Not) Game Genres, pt. 14: John Nesky's 2D Game Solid Boundary Types

Taxonomy of Virtual Spaces

In 2022, John Nesky (Feel Engineer on Journey (Thatgamecompany, 2012)) wrote a Twitter thread analyzing various stylistic choices a game artist may make when designing the boundaries of a 2-D game (like many 2-D platformer games). He preserved the thread as a Google document and in pdf format for easy reference.

2D Game Solid Boundary Types by John Nesky

Nesky's analysis of visual styles has some crossover with my current work in analyzing the spatial paradigms of many platformer games. Each example image (see illustration above) features Samus Aran from Super Metroid (Nintendo, 1994) in an environment constructed by Nesky according to these different stylistic techniques. His design study tends to focus on 2-D platformers, but he also shows how the techniques work for other types of games.

2D Game Solid Boundary Types

Nesky defines 10 different art styles used convey the "fourth wall" through which the player views the game environment. The world is often presented as if in an architectural cross-sectional view, using the game's plane of action as the cutting plane. The navigable area of the game's environment is clearly rendered, but the internal structure of that environment (inside the walls, floors, and ceilings) may be abstracted (surface layer), hidden (silhouette), or stylistically presented (wide open spaces).

1. Modular Blocks
2. Flat Façade
3. Jutting Floor
4. Surface Layer
5. Deep Shadows
6. Silhouette
7. Perspective
8. Fake Perspective
9. Wide Open Spaces
10. Thin Walls

Most of these styles are designed around the capabilities of tile-based environment graphics, like those seen in earlier game consoles like NES, SMS, SNES, and Genesis. These styles do not take foreground or background elements into consideration. They only focus on the environment along the game's plane of action.

Analyzing the Analysis

There are three types of projection methods here that line up with my Taxonomy of Virtual Spaces.

Modular Blocks by John Nesky

Orthographic (Modular Blocks, Flat Façade, Jutting Floor, Surface Layer, Deep Shadows, Silhouette, Wide Open Spaces, Thin Walls)

For my purposes of analyzing spatiality, most of the the styles here are different methods of orthographic projection. The examples above all use a side elevation projection for the environment. Styles like Wide Open Spaces and Jutting Floor do convey a small sense of depth, as if the floors or environmental elements break through space into a foreground layer. However, this projection method tends to convey to the viewer that this is a flat space.

Fake Perspective by John Nesky

Oblique (various) (Fake Perspective)

Nesky's Fake Perspective examples each show the receding lines of the game environment's ground plane (or in the case of The Legend of Zelda: A Link to the Past, the dungeon walls). There are several different projection techniques in these examples.

Yoshi's Island uses a vertical oblique projection, where the side face of the front "wall" is flatly rendered orthogonally and the receding lines of the floor plane are rendered vertically (compare to Yo! Noid on my previous post).

Two games use different oblique projections to render a naive perspective view and a sense of depth: Yoshi's Story (elevation oblique) and Link to the Past (planometric oblique). The receding oblique lines in Yoshi's Story are mirrored left and right, creating an illusion that the lines are converging towards the horizon line. Link to the Past similarly mirrors its oblique lines at the corners of the room to convey a similar illusion. These are not true perspective renderings, though they use some of the same visual cues of a perspective projection.

Nesky's own example is also naive perspective, but the receding lines of the short wall in front of the player avatar appears to be inverted naive perspective: the receding lines diverge into the background instead of converging.

Perspective by John Nesky

Perspectival (usually 1-point) (Perspective)

Curiously, Nesky's first example is a vertical oblique projection and is not truly perspectival at all. This is a paraline projection and receding lines do not coverge in the distance.

Nesky's other Perspective examples are presented in 1-point perspective. Metroid Dread and Link Between Worlds both use full 3-D environments with the camera perpendicular to the back wall (Metroid) or the floor (Zelda). Both games usually retain a fairly flat view of their environments to mirror the gameplay standards of earlier 2-D games in their respective series. Being fully 3-D environments, the camera is also free to tilt and pivot to more dramatic angles as needed, breaking into 2-point or 3-point perspective.

The other example is Contra III, a game I referenced in my previous post). This scene also uses 1-point perspective, although this Super Nintendo title uses a tiled background and no true 3-D models. Another Twitter user joined Nesky's thread and asked, "Why isn't the Contra III example here Fake Perspective?"

Contrast the receding lines of Contra III and Link to the Past environments

I responded to the question with the above altered screen shots and stated that one can trace the receding lines of the environment to see if they converge. Contra III's lines converge almost perfectly on the center of the screen. Each line is projected at a different angle. In contrast, Link to the Past uses a naive perspective technique with the receding lines of each corner of the environment projected obliquely at about 45° from the horizontal. This offers a convincing sense of depth and is fully in line with the art style of the original Legend of Zelda, but it is not a true 1-point perspective.

Odds and Ends

Nesky also gives several separate games as examples of specific uses of these techniques that I think are worth mentioning as they overlap with my research (especially since these are two of my favorite games).

The Legend of Zelda: A Link to the Past

Nesky notes that Link to the Past uses different projection methods for indoor and outdoor environments. He refers to outdoor projection as orthographic, which I define as orthogonal (a classic "top down" view as opposed to a direct overhead view). He does note the unusual fact that you can see the horizon from the pyramid, something that should be impossible from a planometric projection! This is another example where the conceptual image plane of the background is rendered differently from the environment (see here and here).

Horizontal oblique projection in Flashback

Nesky also notes that Flashback's projection is "angled sideways," or in what is called a horizontal oblique projection. As he states, "This visually preserves precise vertical distances while adding depth to the world. Door frames and platform railings are rendered in front of the avatar." There are many doors in Flashback and this aspect is important to making them look like doors instead of walls.

Conclusion

Nesky is not an expert on the technical details of different projection methods, and he fully admits that is the case. But this was never the point of his study. His study focuses on the specific stylistic choices that game artists use (especially those making tile-based "pixel art" games) to define that invisible fourth wall that is coplanar to the player's screen. He has created another method of defining and grouping games by their aesthetic choices rather than purely by technical or genre classifications and I applaud his work.

Digital Project Plans Part II

Taxonomy of Virtual Spaces Part II

Over the summer of 2024, I returning to my prototype digital project to explore the planar geometric projection options that I concluded last summer, named for my Taxonomy of Digital Spaces framework and vocabulary for analyzing the different visuo-spatial configurations of virtual spaces (spatial paradigms) in digital games. 

Link to itch.io prototype build that is playable in browser.

The prototype build simulates the "Filmation" spatial paradigm featured in many popular computer games in the UK in the 1980s, 1990s, and is having something of a resurgence today. The game's projection method can be changed on the fly by pressing the "T" key. 

This year's goal is to incorporate spatial paradigms seen in side scrolling platformers, run-n-gun games, and other influential game genres. These stylistic differences in game graphics can change a player's sense of space as they navigate their avatar through a virtual world.

Take Super Mario Bros. as an example. The graphical presentation is very flat, with every game object and environment tile rendered in an orthographic projection. The virtual space has very little sense of depth and Mario's feet land on the top edge of a ground tile.

Super Mario Bros. (Nintendo, 1985)

However, surviving design documentation shows that SMB creators had a vertical orthogonal (sometimes called vertical oblique) projection method in mind for the environment. This allows the player to see the top surface of the ground plane as well as give a side view of the ground tiles. Mario's feet would land in the middle of a ground surface tile.

Super Mario Bros. design document.

This design document illustration is similar to the spatial paradigm seen in Yo! Noid, where the Noid's feet land near the middle of the ground surface tiles. The receding lines of the ground surface are rendered vertically in parallel on the screen. This appears to give slightly more of a sense of depth than SMB, but still feels fairly flat to me.

Yo! Noid (Capcom, 1990)

Compare this to Super C with its elevation oblique projection of its environment in the platformer-like stages. The receding lines of the ground plane tiles are rendered in parallel at an oblique angle instead of vertical lines. This technique is also used into the near foreground and background, giving a continuous sense of space for some distance in front of and behind the player character's plane of action. The player avatar appears to be running along a wide surface, not a razor-thin plane.

Super C (Konami, 1988)

All three games above were created for the NES (or Famicom in Japan) game console, but each game had different technical capabilities. SMB uses Nintendo's original NROM memory mapper format with 32KB PRG ROM (game program ROM) and only 8KB CHR ROM ("character" or graphics ROM). Yo! Noid uses the MMC1 memory mapper and 128KB PRG/128KB CHR. Super C uses the MMC3 memory mapper and 128KB PRG/128KB CHR. Noid and Super C could feature more varied graphics in different levels throughout the games while SMB was restricted to a mere 8KB of graphics data for the entire game. It is likely that SMB's CHR ROM size restriction was a factor in not using a more complex projection method for rendering the environment.

The three different techniques shown above are examples of paraline projections (receding lines do not converge in the distance). Compare this to the 1-point perspectival projection used in Contra III, shown below. In this boss fight, the receding lines of the environment converge on a single point on the horizon. The player avatar moves along the ground, walls, and ceiling of the inside of a room that appears to recede into the background, with a giant boss enemy emerging from the rear wall. This game was created for the Super NES (Super Famicom) console, which features a faster processor and built-in graphics modes for simulated 3-D effects that are not present in the earlier NES console.

Contra III: The Alien Wars (Konami, 1992)

I will be adding these spatial paradigms and more to my digital project. The player will be able to switch between these paradigms at will while still exploring the same virtual world.

The final goal of my research is to define game aesthetics by their spatial qualities dealing with the embodied phenomenon of navigating virtual spaces, a cyberkinaesthetic experience. I posit that specific aesthetic trends and styles can be traced through our young art form's history and create a new diachronic "art history" of digital games in the process.

Spring 2024 Research Review and Summer 2024 Plans

Spring 2024 Review

Charter on the Preservation of Digital Game Heritage

• While attending GDC (18-22 Mar 2024) I met with numerous members of the game preservation community and discussed my research with them.
• Video Game History Foundation (Frank Cifaldi and Phil Salvador)
• Stanford University Libraries (Henry Lowood)
• The Museum of Art and Digital Entertainment (Jesse Burns and Rob Curl)
• Updated my charter document based on feedback and suggestions
• I presented "A New Charter on the Preservation of Digital Game Heritage" at the MAD (Media, Art and Design) Conference on May the 4th, 2024 (a.k.a. "Star Wars Day").

click image above to view the recording of the presentation

• I have continued revising my charter for submission to the MAD conference proceedings, which is due on 31 Jul 2024.

History of Role-Playing Games

Giving a class lecture covering the contents of my book chapter

• MIT Press published the peer-reviewed book Fifty Years of Dungeons & Dragons on 14 May 2024, including the chapter "Doctor Holmes, I Presume?" that I co-authored with Zach Howard. Our work covers the creation of first "Basic Set" revision of the Dungeons & Dragons rules and its connection to the early RPG scene in California.
• I am also co-teaching a new "History of Role-Playing Games" course and created a new 8-part lecture covering the history of RPGs from the earliest origins in Kriegsspiel and the like, all the way up to digital publishing and the modern ways we play today. My 2nd lecture in the series covers the same information as the book chapter.
• The book chapter and course are described in further detail at my other blog: https://crypticarchivist.blogspot.com/2024/04/book-update-fifty-years-of-dungeons.html
• In service of the new course, I completed an in-depth close reading, analysis, deconstruction, and overhaul of the original D&D rules as published between 1974 and 1975. As an experiential in-class activity, we had the students all play new campaigns using the original rules. However, we didn't want to distribute the original rules due to copyright concerns (even if this is under fair use). Also, we didn't want the students to have to suffer through the original rules that were "slammed together, virtually non-edited" (as per Gary Gygax in Rudy Kraft, "The Wizard of TSR... An Interview with Gary Gygax," Gryphon, Summer, 1980).
• From my analysis, I created my own "retro-clone" named The Fantasy Game. I freely shared the three books I wrote (Character Creation and Combat, Monster Menagerie, and Trove of Treasures) with our students, though any RPG rules that hew close to the original D&D rules would work. The following links have more information about The Fantasy Game project on my other blog:

https://crypticarchivist.blogspot.com/2024/05/introduction-to-fantasy-game-part-1.html

https://crypticarchivist.blogspot.com/2024/05/introduction-to-fantasy-game-part-2.html

Summer 2024 Plans

• Complete my revision of my "A New Charter on the Preservation of Digital Game Heritage" paper for submission to the MAD Conference proceedings (due 31 Jul 2024).
• I will return to my Taxonomy of Virtual Spaces interactive digital project that I started last summer. In the first version of the project, I was able to replicate the "Filmation" spatial paradigm that is part of my theory of spatial aesthetics of digital games. This summer, I will continue the project by adapting other influential spatial paradigms.

(Not) Game Genres, pt. 13: Aki Järvinen's Audiovisual Styles

Taxonomy of Virtual Spaces

Back in 2002, Aki Järvinen of the University of Tampere devised a system for studying various audiovisual styles seen in digital games. He presented his work at his school's Computer Games and Digital Cultures Conference in a paper titled "Gran Stylissimo: The Audiovisual Elements and Styles in Computer and Video Games."

Järvinen's goal is similar to mine: to understand digital games in terms of aesthetic styles rather than game genres or technological achievement. He adapts the concept of "style" from art history "to characterise dominant techniques in [the creation of art] during different historical periods... or... in relation to [a] certain author or 'school'" [2002, pg. 114]. My own concept of spatial paradigms sets out to define patterns and models of knowledge and methods of conveying space in a virtual world. Mine is adapted from Giovanni Dosi's concept of technological paradigms ("Technological Paradigms and Technological Trajectories," Research Policy, 11(3), 1982), which was adapted from Thomas Kuhn's scientific paradigms (The Structure of Scientific Revolutions, 1962).

Audiovisual Elements of Game Environments

Järvinen looks at three different audiovisual "elements" that "can be discerned from all computer and video games."

1. Space/environment ("a football field, for example")
2. Different objects ("characters, things, etc.")
3. Symbols ("point counters, health meters, descriptions, help texts, etc.")

This is a way of dividing up the disparate parts of a digital game screen image, which I argue is always a hybrid amalgam of different image elements. My own system similarly divides the image into three image planes for agents, environment, and background/foreground. This follows the Game FAVR systems three conceptual planes for agents, in-game environment, and off-game environment. Note that Järvinen includes "Symbols," non-diegetic UI and HUD elements that convey information to the player.

Game Environment Construction

Järvinen declares space as the most prominent element in digital games. He further defines the game environment as being built on dimension, points of perception, visual outlook, soundscape, and senso-motority.

Dimension

Essentially, 2-D or 3-D. Isometric "perspective" is mentioned, but it is unclear if he considers this to be a 2-D or 3-D dimensionality.

Point of Perception

"Dimension and point of perception together make up the game environment's rough form. Point of perception is the position from which the player perceives... what goes on in the game environment." This is mostly 1st person, 2nd person (like in text adventure games), or 3rd person views of the game world. Notable is the possibility of "different, co-existing points of perception," such as my system's example of a mini-map.

Note that the categorization of a "point" of perception implies a single, subjective station point from which the environment is observed, likely through linear perspective. In orthogographic, oblique, or axonometric projections, there is no single "point of perception" in which a Cartesian observer may be situated.

Visual Outlook

The dimensionality and PoP are the stage upon which the visual outlook is drawn, down to the textures and polygons. The visual outlook may draw its appearance from other forms of media, especially in adaptations of sports, cartoons, or film properties.

Audiovisual Motifs

These are motifs shared between digital games and other forms of media. Examples are "bullet time" (seen in The Matrix and in Max Payne) and the audiovisuals of a motion tracker device (seen in Aliens and various Aliens vs. Predator games).

Soundscape

The use of diegetic (in-game sounds of the environment and objects in it) and non-diegetic (such as a musical soundtrack) sounds.

Senso-motorism

The means of the player's interactions with the game environment. How does the physical interface of the game work on the player's senses? Elements of haptic feedback, the use of game controller, and such appear to fall under this category.

Select games on a multi-axial audiovisual style spectrum from Gran Stylissimo (Järvinen, 2002)

The Audiovisual Styles

He defines three main audiovisual styles that existing games can be categorized into. Photorealism includes to style subcategories of televisualism and illusionism.

1. Photorealism
1. Televisualism
2. Illusionism
2. Caricaturism
3. Abstractionism

Photorealism aims for highly lifelike, photographic likenesses of objects and environments.

Televisualism aims to reproduce the experience of a television broadcast, often seen in sports games or games that replicate game shows.

Illusionism is for realistically rendered fantastic or imaginary imagery.

Caricaturism is for the look of comic books, cartoons, and caricatures. Notably, the cel-shaded look pioneered by Jet Set Radio belongs here.

Abstractionism does not aim to simulate easily recognizable characters or environments. Many puzzle games, such as Tetris, fall under this category, along with many early games with limited graphics, such as Pong. Other notable abstract titles include Tempest, Vib-Ribbon, and Rez.

Conclusion

Järvinen and I have shared aims, but different approaches to tackling the problem of creating a set of aesthetic styles for digital games. His system uses motifs and visual outlooks to focus on similarities to other forms of media. My system focuses on the intrinsic qualities of digital games and how they embody the player into a virtual environment.