Bernstein basis polynomials: Difference between revisions

Here is ALGOL 60 more nicely printed:

'''procedure''' ''tobern2'' (''a0'', ''a1'', ''a2'', ''b0'', ''b1'', ''b2'');

'''value''' ''a0'', ''a1'', ''a2''; '''comment''' pass by value;

'''real''' ''a0'', ''a1'', ''a2'';

'''real''' ''b0'', ''b1'', ''b2'';

'''comment''' ''Subprogram (1)'': transform monomial coefficients ''a0'', ''a1'', ''a2'' to Bernstein coefficients ''b0'', ''b1'', ''b2'';

'''begin'''

''b0'' := ''a0'';

''b1'' := ''a0'' + ((1/2) × ''a1'');

''b2'' := ''a0'' + ''a1'' + ''a2''

'''end''' ''tobern2'';

'''real''' '''procedure''' ''evalbern2'' (''b0'', ''b1'', ''b2'', ''t'');

'''value''' ''b0'', ''b1'', ''b2'', ''t'';

'''real''' ''b0'', ''b1'', ''b2'', ''t'';

'''comment''' ''Subprogram (2)'': evaluate, at ''t'', the polynomial with Bernstein coefficients ''b0'', ''b1'', ''b2''. Use de Casteljau’s algorithm;

'''begin'''

'''real''' s, ''b01'', ''b12'', ''b012'';

''s'' := 1 - ''t'';

''b01'' := (''s'' × ''b0'') + (''t'' × ''b1'');

''b12'' := (''s'' × ''b1'') + (''t'' × ''b2'');

''b012'' := (''s'' × ''b01'') + (''t'' × ''b12'');

''evalbern2'' := ''b012''

'''end''' ''evalbern2'';

'''procedure''' ''tobern3'' (''a0'', ''a1'', ''a2'', ''a3'', ''b0'', ''b1'', ''b2'', ''b3'');

'''value ''a0'', ''a1'', ''a2'', ''a3'';

'''real''' ''a0'', ''a1'', ''a2'', ''a3'';

'''real''' ''b0'', ''b1'', ''b2'', ''b3'';

'''comment''' ''Subprogram (3)'': transform monomial coefficients ''a0'', ''a1'', ''a2'', ''a3'' to Bernstein coefficients ''b0'', ''b1'', ''b2'', ''b3'';

'''begin'''

''b0'' := ''a0'';

''b1'' := ''a0'' + ((1/3) × ''a1'');

''b2'' := ''a0'' + ((2/3) × ''a1'') + ((1/3) × ''a2'');

''b3'' := ''a0'' + ''a1'' + ''a2'' + ''a3''

'''end''' ''tobern3'';

'''real''' '''procedure''' ''evalbern3'' (''b0'', ''b1'', ''b2'', ''b3'', ''t'');

'''value''' ''b0'', ''b1'', ''b2'', ''b3'', ''t'';

'''real''' ''b0'', ''b1'', ''b2'', ''b3'', ''t'';

'''comment''' ''Subprogram (4)'': evaluate, at ''t'', the polynomial with Bernstein coefficients ''b0'', ''b1'', ''b2'', ''b3''. Use de Casteljau's algorithm;

'''begin'''

'''real''' ''s'', ''b01'', ''b12'', ''b23'', ''b012'', ''b123'', ''b0123'';

''s'' := 1 - ''t'';

''b01'' := (''s'' × ''b0'') + (''t'' × ''b1'');

''b12'' := (''s'' × ''b1'') + (''t'' × ''b2'');

''b23'' := (''s'' × ''b2'') + (''t'' × ''b3'');

''b012'' := (''s'' × ''b01'') + (''t'' × ''b12'');

''b123'' := (''s'' × ''b12'') + (''t'' × ''b23'');

''b0123'' := (''s'' × ''b012'') + (''t'' × ''b123'');

''evalbern3'' := ''b0123''

'''end''' ''evalbern3'';

'''procedure''' bern2to3 (''q0'', ''q1'', ''q2'', ''c0'', ''c1'', ''c2'', ''c3'');

'''value''' ''q0'', ''q1'', ''q2'';

'''real''' ''q0'', ''q1'', ''q2;

'''real''' ''c0'', ''c1'', ''c2'', ''c3'';

'''comment''' ''Subprogram (5)'': transform the quadratic Bernstein coefficients ''q0'', ''q1'', ''q2'' to the cubic Bernstein coefficients ''c0'', ''c1'', ''c2'', ''c3'';

'''begin'''

''c0'' := ''q0'';

''c1'' := ((1/3) × ''q0'') + ((2/3) × ''q1'');

''c2'' := ((2/3) × ''q1'') + ((1/3) × ''q2'');

''c3'' := ''q2''

'''end''' ''bern2to3'';