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1 Dr. Scott Schaefer 3D Transformations
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2/149 Review – Vector Operations Dot Product
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3/149 Review – Vector Operations Dot Product
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4/149 Review – Vector Operations Dot Product
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5/149 Review – Vector Operations Cross Product
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6/149 Review – Vector Operations Cross Product
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7/149 Review – Vector Operations Cross Product
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8/149 Review – Vector Operations Cross Product
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9/149 Review – Vector Operations Cross Product
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10/149 Review – Vector Operations Cross Product
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11/149 Review – Vector Operations Cross Product
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12/149 Review – Vector Operations Cross Product
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13/149 Review – Vector Operations Cross Product
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14/149 Transformations Affine Transformations Translation Uniform Scaling Non-uniform Scaling Rotation Mirror Image Projections Orthogonal Perspective
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15/149 Translation
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16/149 Uniform Scaling
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17/149 Uniform Scaling
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18/149 Uniform Scaling
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19/149 Non-Uniform Scaling
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20/149 Non-Uniform Scaling
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21/149 Non-Uniform Scaling
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22/149 Non-Uniform Scaling
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23/149 Non-Uniform Scaling
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24/149 Non-Uniform Scaling
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25/149 Rotation
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26/149 Rotation
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27/149 Rotation
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28/149 Rotation
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29/149 Rotation
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30/149 Rotation
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31/149 Rotation
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32/149 Rotation
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33/149 Rotation
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34/149 Mirror Image
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35/149 Mirror Image
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36/149 Mirror Image
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37/149 Mirror Image
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38/149 Mirror Image
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39/149 Mirror Image Exactly the same as non-uniform scaling with !!!
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40/149 Orthogonal Projection
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41/149 Orthogonal Projection
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42/149 Orthogonal Projection
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43/149 Orthogonal Projection
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44/149 Orthogonal Projection
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45/149 Orthogonal Projection
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46/149 Perspective Projection
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47/149 Perspective Projection Plane:
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48/149 Perspective Projection Plane: Line:
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49/149 Perspective Projection Plane: Line:
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50/149 Perspective Projection Plane: Line:
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51/149 Perspective Projection Plane: Line:
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52/149 Perspective Projection
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53/149 Perspective Projection
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54/149 Perspective Projection
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55/149 Perspective Projection
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56/149 Perspective Projection Perspective Projection is not defined for vectors!!!
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57/149 Transformations as Matrices Exactly like 2D 4x4 matrices Requires coordinates….
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58/149 Review – Vector Operations Dot Product
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59/149 Review – Vector Operations Dot Product
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60/149 Review – Vector Operations Cross Product
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61/149 Review – Vector Operations Cross Product
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62/149 Review – Vector Operations Cross Product
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63/149 Review – Vector Operations
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64/149 Review – Vector Operations
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65/149 Review – Vector Operations
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66/149 Translation
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67/149 Translation
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68/149 Uniform Scaling
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69/149 Uniform Scaling
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70/149 Uniform Scaling
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71/149 Uniform Scaling
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72/149 Uniform Scaling o = (0,0,0) T
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73/149 Non-Uniform Scaling
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74/149 Non-Uniform Scaling
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75/149 Non-Uniform Scaling
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76/149 Non-Uniform Scaling
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77/149 Non-Uniform Scaling
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78/149 Non-Uniform Scaling v = (1,0,0) T, o = (0,0,0) T
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79/149 Rotation
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80/149 Rotation
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81/149 Rotation
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82/149 Rotation
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83/149 Rotation
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84/149 Rotation
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85/149 Rotation
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86/149 Rotation
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87/149 Rotation
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88/149 Rotation Rotation about x
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89/149 Rotation Rotation about y
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90/149 Rotation Rotation about z
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91/149 Mirror Image
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92/149 Mirror Image
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93/149 Mirror Image
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94/149 Mirror Image
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95/149 Mirror Image
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96/149 Mirror Image
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97/149 v = (0,0,1) T, o = (0,0,0) T Mirror Image
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98/149 Orthogonal Projection
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99/149 Orthogonal Projection
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100/149 Orthogonal Projection
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101/149 Orthogonal Projection
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102/149 Orthogonal Projection
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103/149 Orthogonal Projection
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104/149 Orthogonal Projection v = (0,0,1) T, o = (0,0,0) T
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105/149 Perspective Projection
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106/149 Perspective Projection
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107/149 Perspective Projection
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108/149 Perspective Projection Perspective transformations are not Affine!!! Rational expression requires a slight modification (homogeneous coordinates)
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109/149 Perspective Projection Perspective transformations are not Affine!!! Rational expression requires a slight modification (homogeneous coordinates)
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110/149 Perspective Projection Perspective transformations are not Affine!!! Rational expression requires a slight modification (homogeneous coordinates)
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111/149 Perspective Projection Perspective transformations are not Affine!!! Rational expression requires a slight modification (homogeneous coordinates) 3D location is
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112/149 Perspective Projection
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113/149 Perspective Projection
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114/149 Perspective Projection e = (0,0,1) T, o = (0,0,0) T, v = (0,0,1) T
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115/149 Hierarchical Animation Tree of transformation matrices Each node stores a local transformation with respect to its parent
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116/149 Hierarchical Animation Tree of transformation matrices Each node stores a local transformation with respect to its parent
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117/149 Hierarchical Animation Tree of transformation matrices Each node stores a local transformation with respect to its parent
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118/149 Hierarchical Animation Tree of transformation matrices Each node stores a local transformation with respect to its parent
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119/149 Skeletal Animation
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120/149 Skeletal Animation
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121/149 Skeletal Animation : Bone Transformation
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122/149 Skeletal Animation : Skin Weights : Bone Transformation
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123/149 Skeletal Animation : Skin Weights : Bone Transformation Image taken from [Wang et al. 2002]
![123/149 Skeletal Animation : Skin Weights : Bone Transformation Image taken from [Wang et al. 2002]](http://images.slideplayer.com./32/9996247/slides/slide_123.jpg "123/149 Skeletal Animation : Skin Weights : Bone Transformation Image taken from [Wang et al. 2002]")
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124/149 Skeletal Animation Examples
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125/149 Skeletal Animation Examples
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126/149 Skeletal Animation Examples
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127/149 Transformations in OpenGL Types of transformation matrices View Model Projection Viewport
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128/149 Types of transformation matrices View Model Projection Viewport Transformations in OpenGL
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129/149 Transformations in OpenGL Types of transformation matrices View Model Projection Viewport
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130/149 Transformations in OpenGL Types of transformation matrices View Model Projection Viewport
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131/149 Transformations in OpenGL Types of transformation matrices View Model Projection Viewport
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132/149 OpenGL: Matrix Commands glTranslatef(x, y, z) glScalef(x, y, z) glRotatef(theta, vx, vy, vz) glLoadIdentity(void) glPushMatrix(void)/glPopMatrix(void)
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133/149 OpenGL: Matrix Example glTranslatef(0, 1, 3)
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134/149 OpenGL: Matrix Example glTranslatef(0, 1, 3) glRotatef(45, 0, 1, 0)
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135/149 OpenGL: Matrix Example glTranslatef(0, 1, 3) glRotatef(45, 0, 1, 0) glScalef(1, 1, 2)
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136/149 OpenGL: Matrix Example glTranslatef(0, 1, 3) glRotatef(45, 0, 1, 0) glScalef(1, 1, 2) OpenGL multiplies matrices in the opposite order of what you might expect
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137/149 Coordinate Systems in OpenGL
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138/149 Coordinate Systems in OpenGL
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139/149 Coordinate Systems in OpenGL
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140/149 Coordinate Systems in OpenGL
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141/149 Coordinate Systems in OpenGL
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142/149 Coordinate Systems in OpenGL
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143/149 Coordinate Systems in OpenGL
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144/149 Coordinate Systems in OpenGL
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145/149 Coordinate Systems in OpenGL
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146/149 Coordinate Systems in OpenGL 1.PushMatrix 2.Specify viewer using inverse of view transformation 3. PushMatrix 4. Position object with transformations in opposite order of what you would expect 5. PopMatrix 6. PopMatrix
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147/149 Coordinate Systems in OpenGL 1.PushMatrix 2.Specify viewer using inverse of view transformation 3. PushMatrix 4. Position object with transformations in opposite order of what you would expect 5. PopMatrix 6. PopMatrix
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148/149 Coordinate Systems in OpenGL 1.PushMatrix 2.Specify viewer using inverse of view transformation 3. PushMatrix 4. Position object with transformations in opposite order of what you would expect 5. PopMatrix 6. PopMatrix
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149/149 OpenGL: Special Matrix Commands glMatrixMode(GL_MODELVIEW / GL_PROJECTION) gluLookAt(ex, ey, ez, cx, cy, cz, ux, uy, uz) gluPerspective(fov, aspect, near, far) glOrtho(left, right, bottom, top, near, far) glViewport(x, y, w, h)
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151/149 Hierarchical Animation Typically represented as relative joint locations and rotations
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152/149 Hierarchical Animation Typically represented as relative joint locations and rotations
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153/149 Hierarchical Animation Typically represented as relative joint locations and rotations
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154/149 Hierarchical Animation Typically represented as relative joint locations and rotations
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155/149 Hierarchical Animation Typically represented as relative joint locations and rotations
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156/149 Hierarchical Animation Typically represented as relative joint locations and rotations
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