draw a triangle within a single pixel in opengl

Question

Is it possible to draw a triangle within single pixel?

For example, when I specify the co-ordinates of the vertices of the triangle as A(0, 1), B(0, 0) and C(1, 0). I don't see a triangle being rendered at all. I was expecting to see a small triangle fitting within the pixel.

Is there something I am missing?

Answer 1

Is it possible to draw a triangle within single pixel?

No!

You could try evaluate how much of the pixel is covered by the triangle, but there's no way to draw only part of a pixel. A pixel is the smallest unit of a rasterized display device. The pixel is the smallest element. And the pixel density of a display device sets the physical limit on the representable resolution.

The mathematical theory behind it is called "sampling therory" and most importantly you need to know about the so called Nyquist theorem.

Pixels being the ultimately smallest elements of a picture are also the reason why you can't zoom into a picture like they do in CSI:NY, it's simply not possible because there's simply no more information in the picture as there are pixels. (Well, if you have some additional source of information, for example by combining the images taken over a longer period of time and you can estimate the movements, then it actuall is possible to turn temporal information into spatial information, but that's a different story.)

Answer 2

A pixel is a single point how does a triangle fit into a single point?

It is the absolute smallest unit of an image.

Why do you think you can render half a pixel diagonally? A pixel is either on or off, it can't be any other state. What OpenGL specification do you base your assumption on, most 3D libraries will decide to render a pixel based on how much of the sub-pixel information is filled it. But a pixel can't be partially painted, it is either on or off. A pixel is like a light bulb, you can' light up half of a light bulb.

Regardless, the 3D coordinate space represented doesn't map to the 2D space represented by the graphics plane of the camera drawn on the monitor.

Only with specific camera settings and drawing triangles in a 2D plane at a specific distance from the camera can you expect to try and map the 3D coordinates to 2D coordinates in a 1:1 manner, and even then it isn't precise in many cases.

Sub-pixel rendering, doesn't mean what you think it means, it is a technique/algorithm to determine what RGB elements of a pixels to light up and what color to make them, when there are lots of pixels to be lit up, especially in anti-aliasing situations, and the surrounding pixels are taken into consideration, in a 2D rasterized display. There is no way to partially illuminate a single pixel in a shape, sub-pixel rendering just varies the intensity of the color and brightness of a pixel in a more subtle manner. This only works on LCD display. The wikipedia article describes this very well.

You could never draw a triangle in a single pixel in that case either. A triangle will require at minimum 3 pixels to appear as something that might represent a triangle:

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and 6 pixels to represent a rasterized triangle with all three edges represented.

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Answer 3

A pixel is the smallest discrete unit your display can show. Pixels can only have one color.

Therefore, while OpenGL can attempt to render a triangle to half of a pixel, all you will see is either that pixel filled in or that pixel not filled in. Antialiasing can make the filled in color less strong, but the color from a pixel is solid across the entire pixel.

That's simply the nature of a discrete image.