{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/21926"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/21926","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"The comparison and evaluation of different mathematical models for deformation analysis","abstract":"In the analysis of deformations using geodetic techniques, the errors in point positions due to observation errors must be distinguished from movements due to actual deformation. A number of models are available, which offer solutions to this problem. In this study, four of such methods are described and compared: 1. Method using Invariant Functions. 2. Method using Direct Comparison of Co-ordinates. 3. Method using Direct Differences. 4. Method using Niemeier's Comparison of Co-ordinates. The introduction of \"false\" deformations, caused by errors in translation, rotation and scale, is a very real problem which may be eliminated by processes such as the use of invariant functions (distances and angles) and the sound construction of constraint points. Niemeier's solution to this problem is the use of a free network adjustment which forces the new network into a best fit of the provisional co-ordinates, which generally would be the final co-ordinates of a previous epoch. Although the model advocated for the first three methods above is the minimum constraint adjustment, the free network adjustment may also be used. Similarly, the minimum constraints technique may be employed for Niemeier's method, subject to some necessary modifications. The four methods have thus been compared using both adjustment techniques also. The four methods using both adjustment techniques as well as some variations of methods 1. and 2. above are evaluated using a series of nine simulated test epochs, one reference and eight other, to which known deformations were applied. From the results obtained from the various epochs, the methods are examined for reliability, accuracy and suitability.","abstract_html":"In the analysis of deformations using geodetic techniques, the errors in point positions due to observation errors must be distinguished from movements due to actual deformation. A number of models are available, which offer solutions to this problem. In this study, four of such methods are described and compared: 1. Method using Invariant Functions. 2. Method using Direct Comparison of Co-ordinates. 3. Method using Direct Differences. 4. Method using Niemeier's Comparison of Co-ordinates. The introduction of "false" deformations, caused by errors in translation, rotation and scale, is a very real problem which may be eliminated by processes such as the use of invariant functions (distances and angles) and the sound construction of constraint points. Niemeier's solution to this problem is the use of a free network adjustment which forces the new network into a best fit of the provisional co-ordinates, which generally would be the final co-ordinates of a previous epoch. Although the model advocated for the first three methods above is the minimum constraint adjustment, the free network adjustment may also be used. Similarly, the minimum constraints technique may be employed for Niemeier's method, subject to some necessary modifications. The four methods have thus been compared using both adjustment techniques also. The four methods using both adjustment techniques as well as some variations of methods 1. and 2. above are evaluated using a series of nine simulated test epochs, one reference and eight other, to which known deformations were applied. From the results obtained from the various epochs, the methods are examined for reliability, accuracy and suitability.","abstract_has_math":false,"creators":["Goullee, Robert Jules"],"institution":"School of Architecture, Planning and Geomatics","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Rüther, Heinz","Jackson, J"],"committee_chairs":[],"committee_members":[],"year":1984,"date_issued":"1984","date_published":"1984","updated_at":"2026-07-24T01:33:51Z","subjects":[],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/21926","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Rüther, Heinz","Jackson, J"]},{"key":"dc:creator","label":"Author","values":["Goullee, Robert Jules"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2016-09-25T16:50:28Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2016-09-25T16:50:28Z"]},{"key":"dc:date.issued","label":"Date","values":["1984"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["School of Architecture, Planning and Geomatics"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Cape Town"]},{"key":"dc:type","label":"Dc Type","values":["Master Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Masters"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["MSc (Eng)"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11427/21926"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Bibliography: pages 124-125."]},{"key":"dc:description.abstract","label":"Abstract","values":["In the analysis of deformations using geodetic techniques, the errors in point positions due to observation errors must be distinguished from movements due to actual deformation. A number of models are available, which offer solutions to this problem. In this study, four of such methods are described and compared: 1. Method using Invariant Functions. 2. Method using Direct Comparison of Co-ordinates. 3. Method using Direct Differences. 4. Method using Niemeier's Comparison of Co-ordinates. The introduction of \"false\" deformations, caused by errors in translation, rotation and scale, is a very real problem which may be eliminated by processes such as the use of invariant functions (distances and angles) and the sound construction of constraint points. Niemeier's solution to this problem is the use of a free network adjustment which forces the new network into a best fit of the provisional co-ordinates, which generally would be the final co-ordinates of a previous epoch. Although the model advocated for the first three methods above is the minimum constraint adjustment, the free network adjustment may also be used. Similarly, the minimum constraints technique may be employed for Niemeier's method, subject to some necessary modifications. The four methods have thus been compared using both adjustment techniques also. The four methods using both adjustment techniques as well as some variations of methods 1. and 2. above are evaluated using a series of nine simulated test epochs, one reference and eight other, to which known deformations were applied. From the results obtained from the various epochs, the methods are examined for reliability, accuracy and suitability."]},{"key":"dc:title","label":"Title","values":["The comparison and evaluation of different mathematical models for deformation analysis"]}]}],"canonical_facts":{"dc:contributor.advisor":["Rüther, Heinz","Jackson, J"],"dc:creator":["Goullee, Robert Jules"],"dc:date.accessioned":["2016-09-25T16:50:28Z"],"dc:date.available":["2016-09-25T16:50:28Z"],"dc:date.issued":["1984"],"dc:description":["Bibliography: pages 124-125."],"dc:description.abstract":["In the analysis of deformations using geodetic techniques, the errors in point positions due to observation errors must be distinguished from movements due to actual deformation. A number of models are available, which offer solutions to this problem. In this study, four of such methods are described and compared: 1. Method using Invariant Functions. 2. Method using Direct Comparison of Co-ordinates. 3. Method using Direct Differences. 4. Method using Niemeier's Comparison of Co-ordinates. The introduction of \"false\" deformations, caused by errors in translation, rotation and scale, is a very real problem which may be eliminated by processes such as the use of invariant functions (distances and angles) and the sound construction of constraint points. Niemeier's solution to this problem is the use of a free network adjustment which forces the new network into a best fit of the provisional co-ordinates, which generally would be the final co-ordinates of a previous epoch. Although the model advocated for the first three methods above is the minimum constraint adjustment, the free network adjustment may also be used. Similarly, the minimum constraints technique may be employed for Niemeier's method, subject to some necessary modifications. The four methods have thus been compared using both adjustment techniques also. The four methods using both adjustment techniques as well as some variations of methods 1. and 2. above are evaluated using a series of nine simulated test epochs, one reference and eight other, to which known deformations were applied. From the results obtained from the various epochs, the methods are examined for reliability, accuracy and suitability."],"dc:identifier.uri":["http://hdl.handle.net/11427/21926"],"dc:language.iso":["eng"],"dc:publisher.department":["School of Architecture, Planning and Geomatics"],"dc:publisher.institution":["University of Cape Town"],"dc:title":["The comparison and evaluation of different mathematical models for deformation analysis"],"dc:type":["Master Thesis"],"dc:type.qualificationlevel":["Masters"],"dc:type.qualificationname":["MSc (Eng)"]},"updated_at":"2026-07-24T01:33:51Z"}