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1 function dnurbs = nrbderiv(nurbs) |
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2 % |
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3 % NRBDERIV: Construct the first derivative representation of a |
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4 % NURBS curve or surface. |
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5 % |
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6 % Calling Sequence: |
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7 % |
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8 % ders = nrbderiv(nrb); |
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9 % |
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10 % Parameters: |
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11 % |
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12 % nrb : NURBS data structure, see nrbmak. |
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13 % |
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14 % ders : A data structure that represents the first |
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15 % derivatives of a NURBS curve or surface. |
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16 % |
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17 % Description: |
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18 % |
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19 % The derivatives of a B-Spline are themselves a B-Spline of lower degree, |
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20 % giving an efficient means of evaluating multiple derivatives. However, |
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21 % although the same approach can be applied to NURBS, the situation for |
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22 % NURBS is a more complex. I have at present restricted the derivatives |
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23 % to just the first. I don't claim that this implentation is |
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24 % the best approach, but it will have to do for now. The function returns |
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25 % a data struture that for a NURBS curve contains the first derivatives of |
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26 % the B-Spline representation. Remember that a NURBS curve is represent by |
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27 % a univariate B-Spline using the homogeneous coordinates. |
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28 % The derivative data structure can be evaluated later with the function |
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29 % nrbdeval. |
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30 % |
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31 % Examples: |
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32 % |
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33 % See the function nrbdeval for an example. |
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34 % |
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35 % See: |
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36 % |
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37 % nrbdeval |
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38 |
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39 % D.M. Spink |
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40 % Copyright (c) 2000. |
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41 |
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42 if ~isstruct(nurbs) |
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43 error('NURBS representation is not structure!'); |
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44 end |
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45 |
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46 if ~strcmp(nurbs.form,'B-NURBS') |
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47 error('Not a recognised NURBS representation'); |
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48 end |
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49 |
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50 degree = nurbs.order - 1; |
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51 |
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52 if iscell(nurbs.knots) |
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53 % NURBS structure represents a surface |
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54 |
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55 num1 = nurbs.number(1); |
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56 num2 = nurbs.number(2); |
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57 |
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58 % taking derivatives along the u direction |
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59 dknots = nurbs.knots; |
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60 dcoefs = permute(nurbs.coefs,[1 3 2]); |
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61 dcoefs = reshape(dcoefs,4*num2,num1); |
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62 [dcoefs,dknots{1}] = bspderiv(degree(1),dcoefs,nurbs.knots{1}); |
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63 dcoefs = permute(reshape(dcoefs,[4 num2 size(dcoefs,2)]),[1 3 2]); |
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64 dnurbs{1} = nrbmak(dcoefs, dknots); |
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65 |
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66 % taking derivatives along the v direction |
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67 dknots = nurbs.knots; |
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68 dcoefs = reshape(nurbs.coefs,4*num1,num2); |
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69 [dcoefs,dknots{2}] = bspderiv(degree(2),dcoefs,nurbs.knots{2}); |
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70 dcoefs = reshape(dcoefs,[4 num1 size(dcoefs,2)]); |
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71 dnurbs{2} = nrbmak(dcoefs, dknots); |
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72 |
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73 else |
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74 % NURBS structure represents a curve |
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75 |
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76 [dcoefs,dknots] = bspderiv(degree,nurbs.coefs,nurbs.knots); |
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77 dnurbs = nrbmak(dcoefs, dknots); |
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78 |
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79 end |
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80 |
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81 |
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82 |
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83 |
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84 |
