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If the polygon is specified by its vertices, then this problem is eliminated by checking the y-coordinates of the ray and the ends of the tested polygon side before actual computation of the intersection.
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If and polygon
If the polygon can be drawn on an equally spaced grid such that all its vertices are grid points, Pick's theorem gives a simple formula for the polygon's area based on the numbers of interior and boundary grid points.
If any two simple polygons of equal area are given, then the first can be cut into polygonal pieces which can be reassembled to form the second polygon.
## If that polygon is wholly in front of the plane containing P, move that polygon to the list of nodes in front of P.
## If that polygon is wholly behind the plane containing P, move that polygon to the list of nodes behind P.
## If that polygon is intersected by the plane containing P, split it into two polygons and move them to the respective lists of polygons behind and in front of P.
## If that polygon lies in the plane containing P, add it to the list of polygons at node N.
If the area is sufficiently large, the polygon will not close no matter how accurately measured if it is calculated on a plane.
If the path is a simple path, with no repeated vertices or edges other than the starting and ending vertices, it may also be called a simple cycle, circuit, circle, or polygon ; see Cycle graph.
If it is even, the point lies outside the polygon ; this test also works in three dimensions.
If the point in question is not on the boundary of the polygon, the number of intersections is an even number if the point is outside, and it is odd if inside.
If the ray passes exactly through a vertex of a polygon, then it will intersect 2 segments at their endpoints.
The issue is solved as follows: If the intersection point is a vertex of a tested polygon side, then the intersection counts only if the second vertex of the side lies below the ray.
If the winding number is non-zero, the point lies inside the polygon.
If every internal angle of a simple, closed polygon is less than 180 °, the polygon is called convex.
If the corners of a polygon of size n are all connected to one another, the number of intersections created will be a pentatope number.
If the sides intersect then the polygon is not simple.
If a closed polygonal chain embedded in the plane divides it into two regions one of which is topologically equivalent to a disk, then the chain is called a weakly simple polygon.
If the angle ( rotation ) at which the symmetry occurs divides evenly into a full circle ( 360 °), the result is the helical equivalent of a regular polygon.
If the sequence is correctly constructed, the difference in area between the n-th polygon and the containing shape will become arbitrarily small as n becomes large.
If normal mapping is used, each polygon has many face normals ( the direction a given point on a polygon is facing ), which can be used in tandem with an environment map to produce a more realistic reflection.
If and is
If the circumstances are faced frankly it is not reasonable to expect this to be true.
If his dancers are sometimes made to look as if they might be creatures from Mars, this is consistent with his intention of placing them in the orbit of another world, a world in which they are freed of their pedestrian identities.
If a work is divided into several large segments, a last-minute drawing of random numbers may determine the order of the segments for any particular performance.
If they avoid the use of the pungent, outlawed four-letter word it is because it is taboo ; ;
If Wilhelm Reich is the Moses who has led them out of the Egypt of sexual slavery, Dylan Thomas is the poet who offers them the Dionysian dialectic of justification for their indulgence in liquor, marijuana, sex, and jazz.
If he is the child of nothingness, if he is the predestined victim of an age of atomic wars, then he will consult only his own organic needs and go beyond good and evil.
If it is an honest feeling, then why should she not yield to it??
If he thus achieves a lyrical, dreamlike, drugged intensity, he pays the price for his indulgence by producing work -- Allen Ginsberg's `` Howl '' is a striking example of this tendency -- that is disoriented, Dionysian but without depth and without Apollonian control.
If love reflects the nature of man, as Ortega Y Gasset believes, if the person in love betrays decisively what he is by his behavior in love, then the writers of the beat generation are creating a new literary genre.
If he is good, he may not be legal ; ;
If the man on the sidewalk is surprised at this question, it has served as an exclamation.
If the existent form is to be retained new factors that reinforce it must be introduced into the situation.
If we remove ourselves for a moment from our time and our infatuation with mental disease, isn't there something absurd about a hero in a novel who is defeated by his infantile neurosis??
If many of the characters in contemporary novels appear to be the bloodless relations of characters in a case history it is because the novelist is often forgetful today that those things that we call character manifest themselves in surface behavior, that the ego is still the executive agency of personality, and that all we know of personality must be discerned through the ego.
If he is a traditionalist, he is an eclectic traditionalist.
If our sincerity is granted, and it is granted, the discrepancy can only be explained by the fact that we have come to believe hearsay and legend about ourselves in preference to an understanding gained by earnest self-examination.
If to be innocent is to be helpless, then I had been -- as are we all -- helpless at the start.
If and specified
If they give him advice when he asks it, or if they perform specified duties under his direction, the nature of the U. N. will not of necessity change.
If the symbolic name or actual address of an index word or electronic switch appears or is included in the operand of an XRELEASE or SRELEASE statement ( see page 101 ), the specified index word or electronic switch will again be made available, regardless of the method by which it was reserved.
If the location specified is incorrect, this will cause the computer to write the data to some other part of the program.
If not specified, there's no penalty for a disc landing any height above the ground.
If the XML document depends on parsable external entities ( including the specified external subset, or parsable external entities declared in the internal subset ), it should assert in its XML declaration.
If no range is specified.
If the two input signals are both sinusoids of specified frequencies f < sub > 1 </ sub > and f < sub > 2 </ sub >, then the output of the mixer will contain two new sinsoids that have the sum f < sub > 1 </ sub > + f < sub > 2 </ sub > frequency and the difference frequency absolute value | f < sub > 1 </ sub >-f < sub > 2 </ sub >|.
If the number of counts is not very large, it is more accurate to measure the time interval for a predetermined number of occurrences, rather than the number of occurrences within a specified time.
In a flat d-dimensional space M, at any given time, the configuration of two identical particles can be specified as an element of M × M. If there is no overlap between the particles, so that they do not interact ( at the same time, we are not referring to time delayed interactions here, which are mediated at the speed of light or slower ), then we are dealing with the space
If the lift coefficient for a wing at a specified angle of attack is known ( or estimated using a method such as thin airfoil theory ), then the lift produced for specific flow conditions can be determined using the following equation:
If sending pictures or other easily readable files, most mail clients will display them inline ( unless otherwise specified with the " Content-disposition " header ).
If it is not specified, the
If a great number of attributes end up being the same as on the definition, a great amount of information can be " inherited ", and not have to be redundantly specified in the netlist, saving space, and making the design easier to read by both machines and people.
If no range is specified, the stream is played from the beginning and plays to the end, or, if the stream is paused, it is resumed at the point it was paused.
If all participants are price-takers by definition, then the actor who adjusts prices to eliminate excess demand is not specified ".
If the plaintiff is so determined, a bond may be required, and if the bond requirement is not met within a specified time period, a judgment of dismissal is ordered.
If an XFS filesystem is to be created on a striped RAID array, a stripe unit can be specified when the file system is created.
If the right-hand side is specified as a given function, f ( x, y, z ), i. e., if the whole equation is written as
If a player expends more than the specified increment, then the entire increment is added to the player's clock.
If the rule specifies an AND relationship between the mappings of the two input variables, as the examples above do, the minimum of the two is used as the combined truth value ; if an OR is specified, the maximum is used.
If the Governor fails to return a bill to the legislative house in which it originated within a specified number of days after it was presented to him or her, it becomes a law without their signature.
If the pension benefit fell below a specified level, then such workers were allowed to substitute a wage figure of 75 % of the average wage during this period, thus creating something like a minimum wage benefit.
If it specifies " dBi " or " dBd " then there is no ambiguity, but if only " dB " is specified then the fine print must be consulted.
If a player cannot or does not wish to go all-in, he or she may instead choose to buy chips with cash out-of-pocket at any time, even during the play of a hand, and his bets are limited only by the specified betting structure of the game.
If this option is specified, the < tt >- u </ tt > and < tt >- d </ tt > options are ignored if either or both are also present.
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