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Ontario Tech acknowledges the lands and people of the Mississaugas of Scugog Island First Nation.

We are thankful to be welcome on these lands in friendship. The lands we are situated on are covered by the Williams Treaties and are the traditional territory of the Mississaugas, a branch of the greater Anishinaabeg Nation, including Algonquin, Ojibway, Odawa and Pottawatomi. These lands remain home to many Indigenous nations and peoples.

We acknowledge this land out of respect for the Indigenous nations who have cared for Turtle Island, also called North America, from before the arrival of settler peoples until this day. Most importantly, we acknowledge that the history of these lands has been tainted by poor treatment and a lack of friendship with the First Nations who call them home.

This history is something we are all affected by because we are all treaty people in Canada. We all have a shared history to reflect on, and each of us is affected by this history in different ways. Our past defines our present, but if we move forward as friends and allies, then it does not have to define our future.

Learn more about Indigenous Education and Cultural Services

March 17, 2010

Speaker: Mr. Luis Alberto Zarrabeitia, MSc

Title: Multiresolution terrain representation by level curve elimination

Abstract: The most popular adaptive thinning algorithms for bivariate scattered data sets with corresponding function values are point removal schemes, where the points are recursively removed (1). Since level curves are still the most common form to represent elevation data for the Earth's surface, we propose a new method for computing a multiresolution representation of a digital terrain model using the connectivity information provided by contour lines.

The core of the presented multiresolution method is an algorithm for removing recursively the level curves according to some error criterion. It allows to obtain a sequence of approximations of the terrain where the difference between two consecutive approximations is only one curve: the less "important". In other words, the input curves are sorted in such a way that the n most relevant curves are contained in the n-th resolution level. For a given curve, the relevance criterion is the error computed using a function interpolating the remaining curves. Hence, to fully formulate the multiresolution algorithm it is necessary a function interpolating the contour lines of the terrain. In our method, we define the error measure associated with a level curve by means of the interpolant for terrain models introduced in (2).

To obtain an efficient implementation of the proposed method it was necessary to use adequate data structures and computational geometry algorithms in order to solve several subproblems, for instance the computation of the distance from a point to a polygon (with a huge amount of vertices), the simplification of the level curves and the point location problem.