UNIT 28 - AFFINE AND CURVILINEAR TRANSFORMATIONS

UNIT 28 - AFFINE AND CURVILINEAR TRANSFORMATIONS

  • A. INTRODUCTION
  • B. AFFINE TRANSFORMATION PRIMITIVES
  • C. COMPLEX AFFINE TRANSFORMATIONS
  • D. AFFINE TRANSFORMATIONS IN GIS
  • E. CURVILINEAR TRANSFORMATIONS
  • REFERENCES
  • DISCUSSION AND EXAM QUESTIONS
  • NOTES

    UNIT 28 - AFFINE AND CURVILINEAR TRANSFORMATIONS

    A. INTRODUCTION

    B. AFFINE TRANSFORMATION PRIMITIVES

    1. Translation

    2. Scaling

    3. Rotation

    4. Reflection

    C. COMPLEX AFFINE TRANSFORMATIONS

    D. AFFINE TRANSFORMATIONS IN GIS

    Simple Example

    City Fire Study Example

    E. CURVILINEAR TRANSFORMATIONS

    REFERENCES

    Goodchild, M.F., 1984. "Geocoding and Geosampling," Spatial Statistics and Models, G.L. Gaile and C.J. Willmott, eds., Reidel Publishing Company, Dordrecht, Holland, pp. 33-53.

    DISCUSSION AND EXAM QUESTIONS

    1. A map has been digitized using an origin in the lower left corner. The x axis is the lower edge of the map, and the y axis is the left edge. The study area ranges from 0 to 100 in x, and 0 to 50 in y. Calculate the transformations necessary to show this area on a screen containing 640 columns and 480 rows, with the columns and rows numbered from the top left corner, assuming that positions on the screen are referred to by row and column numbers.

    2. Describe the transformations between x and y and UTM Northing and UTM Easting given in the text of the unit for the fire study example in terms of (a) translation of the origin, (b) scaling, (c) rotation and (d) reflection.

    3. Discuss the factors which contribute to lack of fit between maps of the same area, and failure of affine transformations to register maps perfectly using control points. Discuss the relative importance of each of these factors.

    4. Discuss the criteria you would use to select control points, including the number and distribution of such points, in setting up a coordinate transformation.


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