# Signed Distance Functions: Modeling In Math

What if instead of defining a mesh as a series of vertices and edges in a 3D space, you could describe it as a single function? The easiest function would return the signed distance to the closest point (negative meaning you were inside the object). That’s precisely what a signed distance function (SDF) is. A signed distance field (also SDF) is just a voxel grid where the SDF is sampled at each point on the grid. First, we’ll discuss SDFs in 2D and then jump to 3D.

### SDFs in 2D

A signed distance function in 2D is more straightforward to reason about so we’ll cover it first. Additionally, it is helpful for font rendering in specific scenarios. [Vassilis] of [Render Diagrams] has a beautiful demo on two-dimensional SDFs that covers the basics. The naive technique for rendering is to create a grid and calculate the distance at each point in the grid. If the distance is greater than the size of the grid cell, the pixel is not colored in. Negative values mean the pixel is colored in as the center of the pixel is inside the shape. By increasing the size of the grid, you can get better approximations of the actual shape of the SDF. So, why use this over a more traditional vector approach? The advantage is that the shape is represented by a single formula calculated at many points. Most modern computers are extraordinarily good at calculating the same thing thousands of times with slightly different parameters, often using the GPU. GLyphy is an SDF-based text renderer that uses OpenGL ES2 as a shader, as discussed at Linux conf in 2014. Freetype even merged an SDF renderer written by [Anuj Verma] back in 2020. Continue reading “Signed Distance Functions: Modeling In Math”

# OpenGL In 500 Lines (Sort Of…)

How difficult is OpenGL? How difficult can it be if you can build a basic renderer in 500 lines of code? That’s what [Dmitry] did as part of a series of tiny applications. The renderer is part of a course and the line limit is to allow students to build their own rendering software. [Dmitry] feels that you can’t write efficient code for things like OpenGL without understanding how they work first.

For educational purposes, the system uses few external dependencies. Students get a class that can work with TGA format files and a way to set the color of one pixel. The rest of the renderer is up to the student guided by nine lessons ranging from Bresenham’s algorithm to ambient occlusion. One of the last lessons switches gears to OpenGL so you can see how it all applies.

# Ray Casting 101 Makes Things Simple

[SSZCZEP] had a tough time understanding ray tracing to create 3D-like objects on a 2D map. So once he figured it out, he wrote a tutorial he hopes will be more accessible for those who may be struggling themselves.

If you’ve ever played Wolfenstein 3D you’ll have seen the technique, although it crops up all over the place. The tutorial borrows an animated graphic from [Lucas Vieira] that really shows off how it works in a simplified way. The explanation is pretty simple. From a point of view — that is a camera or the eyeball of a player — you draw rays out until they strike something. The distance and angle tell you how to render the scene. Instead of a camera, you can also figure out how a ray of light will fall from a light source.

There is a bit of math, but also some cool interactive demos to drive home the points. We wondered if Demos 3 and 4 reminded anyone else of an obscure vector graphics video game from the 1970s? Most of the tutorial is pretty brute force, calculating points that you can know ahead of time won’t be useful. But if you stick with it, there are some concessions to optimization and pointers to more information.

Overall, a lot of good info and cool demos if this is your sort of thing. While it might not be the speediest, you can do ray tracing on our old friend the Arduino. Or, if you prefer, Excel.

# A Look At How Nintendo Mastered Dual Screens

When it was first announced, many people were skeptical of the Nintendo DS. Rather than pushing raw power, the unique dual screen handheld was designed to explore new styles of play. Compared to the more traditional handhelds like the Game Boy Advance (GBA) or even Sony’s PlayStation Portable (PSP), the DS seemed like huge gamble for the Japanese gaming giant.

But it paid off. The Nintendo DS ended up being one of the most successful gaming platforms of all time, and as [Modern Vintage Gamer] explains in a recent video, at least part of that was due to its surprising graphical prowess. While it was technically inferior to the PSP in almost every way, Nintendo’s decades of experience in pushing the limits of 2D graphics allowed them to squeeze more out of the hardware than many would have thought possible.

On one level, the Nintendo DS could be seen as a upgraded GBA. Developers who were already used to the 2D capabilities of that system would feel right at home when they made the switch to the DS. As with previous 2D consoles, the DS had several screen modes complete with hardware-accelerated support for moving, scaling, rotating, and reflecting up to four background layers. This made it easy and computationally efficient to pull off pseudo-3D effects such as having multiple backdrop images scrolling by at different speeds to convey a sense of depth.

On top of its GBA-inherited tile and sprite 2D engine, the DS also featured a rudimentary GPU responsible for handling 3D geometry and rendering. Hardware accelerated 3D could only used on one screen at a time, which meant most games would keep the closeup view of the action on one display, and used the second panel to show 2D imagery such as an overhead map. But developers did have the option of flipping between the displays on each frame to render 3D on both panels at a reduced frame rate. The hardware can also handle shadows and included integrated support for cell shading, which was a particularly popular graphical effect at the time.

By combining the 2D and 3D hardware capabilities of the Nintendo DS onto a single screen, developers could produce complex graphical effects. [Modern Vintage Gamer] uses the example of New Super Mario Bros, which places a detailed 3D model of Mario over several layers of moving 2D bitmaps. Ultimately the 3D capabilities of the DS were hindered by the limited resolution of its 256 x 192 LCD panels; but considering most people were still using flip phones when the DS came out, it was impressive for the time.

Compared to the Game Boy Advance, or even the original “brick” Game Boy, it doesn’t seem like hackers have had much luck coming up with ways to exploiting the capabilities of the Nintendo DS. But perhaps with more detailed retrospectives like this, the community will be inspired to take another look at this unique entry in gaming history.

# Neural Networks Walk Better Than Humans For Game Animation

Modern day video games have come a long way from Mario the plumber hopping across the screen. Incredibly intricate environments of games today are part of the lure for new gamers and this experience is brought to life by the characters interacting with the scene. However the illusion of the virtual world is disrupted by unnatural movements of the figures in performing actions such as turning around suddenly or climbing a hill.

To remedy the abrupt movements, [Daniel Holden et. al] recently published a paper (PDF) and a video showing a method to greatly improve the real-time character control mechanism. The proposed system uses a neural network that has been trained using a large data set of walking, jumping and other sequences on various terrains. The key is breaking down the process of bipedal movement and its cyclic behaviour into a series of sub-steps or phases. Each phase translates to a natural posture for the character while moving. The system precomputes the next-phases offline to conserve computational resources at runtime. Then considering user control, previous pose of the character(including joint positions) and terrain geometry, the consequent frame of the animation is computed. The computation is done by a regression network that calculates future position of the joints and a blending function is used for Motion Matching as described in a presentation (PDF) and video by [Simon Clavet]. Continue reading “Neural Networks Walk Better Than Humans For Game Animation”

# Better 3D Graphics On The Arduino

There are cheap LCDs available from China, and when plugged into an Arduino, these displays serve as useful interfaces or even shinier baubles for your latest project. [Michael] picked up a few of these displays in the hope of putting a few animated .GIFs on them. This is an impossible task with an ATMega microcontroller – the Arduino does not have the RAM or the processing power to play full-screen animations. It is possible to display 3D vector graphics, with an updated graphics library [Michael] wrote.

The display in question uses the ILI9341 LCD driver, found in the Adafruit library, and an optimized 3D graphics driver. Both of these drivers have noticeable flicker when the animation updates, caused by the delay between erasing a previous frame and when a new frame is drawn.

With 16-bit color and a resolution of 320×240 pixels, there simply isn’t enough memory or the processing power on an ATMega microcontroller to render anything in the time it takes to display a single frame. There isn’t enough memory to render off-screen, either. To solve this problem, [Michael] built his render library to only render pixels that are different from the previous frame.

Rendering in 3D presents its own problems, with convex surfaces that can overlap themselves. To fix this, [Michael]’s library renders objects from front to back – if the pixel doesn’t change, it doesn’t need to be rendered. This automatically handles occlusions.

In a demo application, [Michael]’s LCD and Arduino can display the Stanford bunny, a low-poly 3D face, and geometric object. It’s not a video game yet, but [Michael] thinks he can port the classic game Spectre to this platform and have it run at a decent frame rate.

Video of the demo below.

# Open Source GPU Released

Nearly a year ago, an extremely interesting project hit Kickstarter: an open source GPU, written for an FPGA. For reasons that are obvious in retrospect, the GPL-GPU Kickstarter was not funded, but that doesn’t mean these developers don’t believe in what they’re doing. The first version of this open source graphics processor has now been released, giving anyone with an interest a look at what a late-90s era GPU looks like on the inside, If you’re cool enough, there’s also enough supporting documentation to build your own.

A quick note for the PC Master Race: this thing might run Quake eventually. It’s not a powerhouse. That said, [Bunnie] had a hard time finding an open source GPU for the Novena laptop, and the drivers for the VideoCore IV in the Raspi have only recently been open sourced. A completely open GPU simply doesn’t exist, and short of a few very, very limited thesis projects there hasn’t been anything like this before.

Right now, the GPL-GPU has 3D graphics acceleration working with VGA on a PCI bus. The plan is to update this late-90s setup to interfaces that make a little more sense, and add DVI and HDMI output. Not bad for a failed Kickstarter, right?