Roman Polański is a French-Polish film director, producer and actor. His Polish-Jewish parents moved the family back from Paris to Kraków in 1937. Two years Poland was invaded by Nazi Germany starting World War II and the Polanskis found themselves trapped in the Kraków Ghetto. After his mother and father were taken in raids, Polanski spent his formative years in foster homes under an adopted identity, trying to survive the Holocaust. Polanski's first feature-length film, Knife in the Water, was made in Poland and was nominated for a United States Academy Award for Best Foreign Language Film, he has since received five more Oscar nominations, along with two BAFTAs, four Césars, a Golden Globe Award and the Palme d'Or of the Cannes Film Festival in France. In the United Kingdom he directed three films, beginning with Repulsion. In 1968, he moved to the United States and cemented his status by directing the horror film Rosemary's Baby. A turning point in his life took place in 1969, when his pregnant wife, Sharon Tate, four friends were brutally murdered by members of the Manson Family.

Following her death, Polanski returned to Europe and continued directing. He made Macbeth in England and back in Hollywood, nominated for eleven Academy Awards. In 1977, Polanski was charged with drugging and raping a 13-year-old girl, he subsequently pled guilty to the lesser offence of unlawful sex with a minor. After spending 42 days undergoing psychiatric evaluation in prison in preparation for sentencing, who had expected to be put on probation, fled to Paris after learning that the judge planned to reject his plea deal and impose a prison term. In Europe, Polanski continued starring Nastassja Kinski, it won France's César Awards for Best Picture and Best Director, received three Oscars. He produced and directed The Pianist, a drama about a Jewish-Polish musician escaping Nazi persecution, starring Adrien Brody and Emilia Fox; the film won three Academy Awards including Best Director, along with numerous international awards. He directed Oliver Twist, a story which parallels his own life as a "young boy attempting to triumph over adversity".

He was awarded Best Director for The Ghost Writer at the 23rd European Film Awards. He received Best Screenwriter nomination at the aforementioned awards for Carnage. In 2018, the Academy of Motion Picture Arts and Sciences voted to expel Polanski from its membership. Polanski was born in Paris. Polański's father was Jewish and from Poland, his mother had Annette, by her previous husband. Annette managed to survive Auschwitz, where her mother died, left Poland forever for France. Polański's parents were both agnostics. Polański stated "I'm an atheist" in an interview about Rosemary's Baby; the Polański family moved back to the Polish city of Kraków in early 1937, were living there when World War II began with the invasion of Poland. Kraków was soon occupied by the German forces, the racist and anti-Semitic Nuremberg Laws made the Polańskis targets of persecution, forcing them into the Kraków Ghetto, along with thousands of the city's Jews. Around the age of six, he attended primary school for only a few weeks, until "all the Jewish children were abruptly expelled," writes biographer Christopher Sandford.

That initiative was soon followed by the requirement that all Jewish children over the age of twelve wear white armbands with a blue Star of David imprinted for visual identification. After he was expelled, he would not be allowed to enter another classroom for the next six years. Polanski witnessed both the ghettoization of Kraków's Jews into a compact area of the city, the subsequent deportation of all the ghetto's Jews to German death camps, he watched. He remembers from age six, one of his first experiences of the terrors to follow: I had just been visiting my grandmother... when I received a foretaste of things to come. At first I didn't know. I saw people scattering in all directions. I realized why the street had emptied so quickly; some women were being herded along it by German soldiers. Instead of running away like the rest, I felt compelled to watch. One older woman at the rear of the column couldn't keep up. A German officer kept prodding her back into line, but she fell down on all fours...

A pistol appeared in the officer's hand. There was a loud bang, blood came welling out of her back. I ran straight into the nearest building, squeezed into a smelly recess beneath some wooden stairs, didn't come out for hours. I developed a strange habit: clenching my fists so hard. I woke up one morning to find that I had wet my bed, his father was transferred, along with thousands of other Jews, to Mauthausen, a group of 49 German concentration camps in Austria. His mother was taken to Auschwitz, was killed soon after arriving; the forced exodus took place after the German liquidation of the Warsaw Ghetto, a true-life backdrop to Polanski's film The Pianist. Polanski, hiding from the Germans, remembered seeing his father being marched off with a long line of people. Polanski tried getting closer to his father to ask him what was happening, managed to get within a few

The Dimensionally Extended nine-Intersection Model is a topological model and a standard used to describe the spatial relations of two regions, in geometry, point-set topology, geospatial topology, fields related to computer spatial analysis. The spatial relations expressed by the model are invariant to rotation and scaling transformations; the matrix provides an approach for classifying geometry relations. Speaking, with a true/false matrix domain, there are 512 possible 2D topologic relations, that can be grouped into binary classification schemes; the English language contains about 10 schemes, such as "intersects", "touches" and "equals". When testing two geometries against a scheme, the result is a spatial predicate named by the scheme; the model was developed by others based on the seminal works of Egenhofer and others. It has been used as a basis for standards of queries and assertions in geographic information systems and spatial databases; the DE-9IM model is based on a 3×3 intersection matrix with the form: where dim is the dimension of the intersection of the interior and exterior of geometries a and b.

The terms interior and boundary in this article are used in the sense used in algebraic topology and manifold theory, not in the sense used in general topology: for example, the interior of a line segment is the line segment without its endpoints, its boundary is just the two endpoints. In the notation of topological space operators, the matrix elements can be expressed as The dimension of empty sets are denoted as −1 or F; the dimension of non-empty sets are denoted with the maximum number of dimensions of the intersection 0 for points, 1 for lines, 2 for areas. The domain of the model is. A simplified version of dim ⁡ values are obtained mapping the values to T, so using the boolean domain; the matrix, denoted with operators, can be expressed as The elements of the matrix can be named as shown below: Both matrix forms, with dimensional and boolean domains, can be serialized as "DE-9IM string codes", which represent them in a single-line string pattern. Since 1999 the string codes have a standard format.

For output checking or pattern analysis, a matrix value can be checked by a "mask": a desired output value with optional asterisk symbols as wildcards — that is, "*" indicating output positions that the designer does not care about. The domain of the mask elements is, or for the boolean form; the simpler models 4-Intersection and 9-Intersection were proposed before DE-9IM for expressing spatial relations. They can be used instead of the DE-9IM to optimize computation when input conditions satisfy specific constraints. Visually, for two overlapping polygonal geometries, this looks like: Reading from left-to-right and top-to-bottom, the DE-9IM string code is'212101212', the compact representation of I I = 2, I B = 1, I E = 2, B I = 1, B B = 0, B E = 1, E I = 2, E B = 1, E E = 2. Spatial predicates are topologically-invariant binary spatial relations based on the DE-9IM. For ease of use "named spatial predicates" have been defined for some common relations; the spatial predicate functions that can be derived from DE-9IM include:Predicates defined with masks of domain Predicates that can be obtained from the above by logical negation or parameter inversion, as indicated by the last column: Predicates that utilize the input dimensions, are defined with masks of domain Notice that: The topologically equal definition does not imply that they have the same points or that they are of the same class.

The output of D E - 9 I M ⁡ have the information contained in a list of all interpretable predicates about geometries a and b. All predicates are computed by masks. Only Crosses and Overlaps have additional conditions about dim ⁡ and dim ⁡. All mask string codes end with *; this is because EE is trivially true, thus provides no useful information. The Equals mask, T*F**FFF*, is the "merge" of Contains and Within: ∧; the mask T ***** FF * occurs in the definition of both Covers. Covers is a more inclusive relation. In particular, unlike Contains it does not distinguish between points in the boundary and in the interior of geometries. For most situations, Covers should be used in preference to Contains; the mask T*F**F*** occurs in the definition of both Within and CoveredBy. For most situations, CoveredBy should be used in preference to Within; the spatial predicates have the following properties of binary relations: Refl

The knockout stage of the 2009 FIFA Confederations Cup began on 24 June and concluded on 28 June 2009 with the final at the Ellis Park Stadium, Johannesburg. It was the second and final stage following the group stage; the top two teams from each group advanced to the knockout stage to compete in a single-elimination style tournament. A third-place match was played between the two losing teams of the semi-finals. In the knockout stage, if a match was level at the end of 90 minutes, extra time of two periods would be played. If the score was still level after extra time, the match would be decided by a penalty shoot-out; the 2009 FIFA Confederations Cup Final was held at Ellis Park Stadium, South Africa, on 28 June 2009 and was contested by the United States and Brazil. This was the first appearance for the United States in the final of a FIFA men's competition; this was Brazil's fourth appearance in a Confederations Cup final. Brazil won their third Confederations Cup title. Prior to the match, FIFA honoured Cameroonian midfielder Marc-Vivien Foé, who died of a heart-related disease during a FIFA Confederations Cup match in 2003.

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