![]() In short, itâs a heavy mental burden to know and use all these rules all the time. (This is false because promotions favor signed types.) For example: Suppose uint8_t x uint8_t y uint32_t z, then x + y should have a type like uint8_t or unsigned int or something reasonable, and +z would still be uint32_t. Whenever all the operand(s) of an arithmetic operator (unary or binary) have unsigned types, the arithmetic operation will be performed in unsigned mode (thus never triggering undefined behavior) and the result type will be unsigned. ) (See type punning and strict aliasing.) Data types Basic integer typesĪ basic integer type is specified using some legal sequence of keywords drawn from the set is safe. By contrast, integer math is a foundation of programming and computer science, and all calculations are always exact in theory (ignoring implementations issues like overflow). Note that floating-point number types will not be discussed at all, because that mostly deals with how to analyze and handle approximation errors that stem from rounding. Whenever I read or write C/C++ code, I need to recall and apply these rules in many situations, such as: Choosing an appropriate type for a local variable / array element / structure field, converting between types, and doing any kind of arithmetic or comparison. In this article, I try to strike a balance between brevity (easing the reader) and completeness (providing absolute correctness and extensive detail). The Javascript source for both the ASCII and canvas rendering is right here.This is my own collection of hard-earned knowledge about how integers work in C/C++, and how to use them carefully and correctly. Since z’ is a fixed constant, and not functionally aĬoordinate, let’s rename it to K 1, so our projection equationīecomes \((x',y') = (\frac So to project a 3D coordinate to 2D, we scale a coordinate by the screenĭistance z’. Thus the relative proportions are maintained: Right triangle, and a similar right triangle is formed with ( x’, y’, z’). To obtain: notice that the origin, the y-axis, and point ( x, y, z) form a We can only see the y and z axes, but the math works the same for the xĪxis (just pretend this is a top view instead). To render a 3D object onto a 2D screen, we project each point ( x, y, z) inģD-space onto a plane located z’ units away from the viewer, so that theĬorresponding 2D position is ( x’, y’). Sitting in front of a screen, viewing a 3D object behind it. The following diagram is a side view of a person So how do we do that? Well, let’s start with the basic math behind 3D Illumination value of the surface at each point: from dimmest to The “pixels” it plots are ASCII characters corresponding to the All it does is plot pixels along the surface of the torus atįixed-angle increments, and does it densely enough that the final result looks Since it’s just rendering relatively low-resolution ASCII art, I massivelyĬheat. )*m-c*d*e-f*g-l the output, animated in Javascript:Īt its core, it’s a framebuffer and a Z-buffer into which I render pixels. Not exactly fresh in my memory, so I will reconstruct it from scratch, in greatĭetail, and hopefully get approximately the same result. Had a couple requests to explain this one. There has been a sudden resurgence of interest in my “donut” code from 2006, and I’ve Donut math: how donut.c works Jul 20, 2011
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