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Dodge is applied when the value on the top layer is lighter than middle gray, and burn applies when the top layer value is darker. The calculation simplifies to the sum of the bottom layer and twice the top layer, subtract 1. This mode decreases the contrast. Subtract: this blend mode sums the value in the two layers and subtracts 1. Unlike ...
A law of Boolean algebra is an identity such as x ∨ (y ∨ z) = (x ∨ y) ∨ z between two Boolean terms, where a Boolean term is defined as an expression built up from variables and the constants 0 and 1 using the operations ∧, ∨, and ¬. The concept can be extended to terms involving other Boolean operations such as ⊕, →, and ≡ ...
The great variety and (relative) complexity of formulas involving set subtraction (compared to those without it) is in part due to the fact that unlike ,, and , set subtraction is neither associative nor commutative and it also is not left distributive over ,, , or even over itself.
Modern implementations for Boolean operations on polygons tend to use plane sweep algorithms (or Sweep line algorithms). A list of papers using plane sweep algorithms for Boolean operations on polygons can be found in References below. Boolean operations on convex polygons and monotone polygons of the same direction may be performed in linear ...
The algebra of sets is the set-theoretic analogue of the algebra of numbers. Just as arithmetic addition and multiplication are associative and commutative, so are set union and intersection; just as the arithmetic relation "less than or equal" is reflexive, antisymmetric and transitive, so is the set relation of "subset".
On the other hand, in the expressions evaluated by #expr and #ifexpr, Boolean operators like and, or, and not interpret the numerical value 0 as false and any other number as true. In terms of output, Boolean operations return 1 for a true value and 0 for false (and these are treated as ordinary numbers by the numerical operators).
A Boolean value is either true or false. A Boolean expression may be composed of a combination of the Boolean constants True/False or Yes/No, Boolean-typed variables, Boolean-valued operators, and Boolean-valued functions. [1] Boolean expressions correspond to propositional formulas in logic and are a special case of Boolean circuits. [2]
A Boolean-valued function (sometimes called a predicate or a proposition) is a function of the type f : X → B, where X is an arbitrary set and where B is a Boolean domain, i.e. a generic two-element set, (for example B = {0, 1}), whose elements are interpreted as logical values, for example, 0 = false and 1 = true, i.e., a single bit of information.