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* src/sdf/ftsdf.c: Use ASCII single quote (').

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Anuj Verma 2020-07-03 18:43:36 +05:30 committed by anujverma
parent ddf631729e
commit 4fcc1653ca
2 changed files with 43 additions and 38 deletions
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5
[GSoC]ChangeLog
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@ -1,3 +1,8 @@
2020-07-03 Anuj Verma <anujv@iitbhilai.ac.in>
* src/sdf/ftsdf.c: Use ASCII single quote (') instead
of back tick (`) for derivatives. Looks cleaner.
2020-07-03 Anuj Verma <anujv@iitbhilai.ac.in>
[sdf] Added function to find shortest distance from a

76
src/sdf/ftsdf.c
View File

@ -1214,14 +1214,14 @@
/* B( t ) = t^2( A ) + 2t( B ) + p0 */
/* */
/* => the derivative of the above equation is written as */
/* B`( t ) = 2( tA + B ) */
/* B'( t ) = 2( tA + B ) */
/* */
/* => now to find the shortest distance from p to B( t ), we */
/* find the point on the curve at which the shortest */
/* distance vector ( i.e. B( t ) - p ) and the direction */
/* ( i.e. B`( t )) makes 90 degrees. in other words we make */
/* ( i.e. B'( t )) makes 90 degrees. in other words we make */
/* the dot product zero. */
/* ( B( t ) - p ).( B`( t ) ) = 0 */
/* ( B( t ) - p ).( B'( t ) ) = 0 */
/* ( t^2( A ) + 2t( B ) + p0 - p ).( 2( tA + B ) ) = 0 */
/* */
/* after simplifying we get a cubic equation as */
@ -1372,7 +1372,7 @@
}
}
/* B`( t ) = 2( tA + B ) */
/* B'( t ) = 2( tA + B ) */
direction.x = 2 * FT_MulFix( aA.x, min_factor ) + 2 * bB.x;
direction.y = 2 * FT_MulFix( aA.y, min_factor ) + 2 * bB.y;
@ -1439,10 +1439,10 @@
/* B( t ) = t^2( A ) + t( B ) + p0 */
/* */
/* => the derivative of the above equation is written as */
/* B`( t ) = 2t( A ) + B */
/* B'( t ) = 2t( A ) + B */
/* */
/* => further derivative of the above equation is written as */
/* B``( t ) = 2A */
/* B''( t ) = 2A */
/* */
/* => the equation of distance from point `p' to the curve */
/* P( t ) can be written as */
@ -1452,7 +1452,7 @@
/* */
/* => finally the equation of angle between curve B( t ) and */
/* point to curve distance P( t ) can be written as */
/* Q( t ) = P( t ).B`( t ) */
/* Q( t ) = P( t ).B'( t ) */
/* */
/* => now our task is to find a value of t such that the above */
/* equation Q( t ) becomes zero. in other words the point */
@ -1462,19 +1462,19 @@
/* => we first assume a arbitary value of the factor `t' and */
/* then we improve it using Newton's equation such as */
/* */
/* t -= Q( t ) / Q`( t ) */
/* t -= Q( t ) / Q'( t ) */
/* putting value of Q( t ) from the above equation gives */
/* */
/* t -= P( t ).B`( t ) / derivative( P( t ).B`( t ) ) */
/* t -= P( t ).B`( t ) / */
/* ( P`( t )B`( t ) + P( t ).B``( t ) ) */
/* t -= P( t ).B'( t ) / derivative( P( t ).B'( t ) ) */
/* t -= P( t ).B'( t ) / */
/* ( P'( t )B'( t ) + P( t ).B''( t ) ) */
/* */
/* P`( t ) is noting but B`( t ) because the constant are */
/* P'( t ) is noting but B'( t ) because the constant are */
/* gone due to derivative */
/* */
/* => finally we get the equation to improve the factor as */
/* t -= P( t ).B`( t ) / */
/* ( B`( t ).B`( t ) + P( t ).B``( t ) ) */
/* t -= P( t ).B'( t ) / */
/* ( B'( t ).B'( t ) + P( t ).B''( t ) ) */
/* */
/* [note]: B and B( t ) are different in the above equations */
@ -1567,24 +1567,24 @@
}
/* This the actual Newton's approximation. */
/* t -= P( t ).B`( t ) / */
/* ( B`( t ).B`( t ) + P( t ).B``( t ) ) */
/* t -= P( t ).B'( t ) / */
/* ( B'( t ).B'( t ) + P( t ).B''( t ) ) */
/* B`( t ) = 2tA + B */
/* B'( t ) = 2tA + B */
d1.x = FT_MulFix( aA.x, 2 * factor ) + bB.x;
d1.y = FT_MulFix( aA.y, 2 * factor ) + bB.y;
/* B``( t ) = 2A */
/* B''( t ) = 2A */
d2.x = 2 * aA.x;
d2.y = 2 * aA.y;
dist_vector.x /= 1024;
dist_vector.y /= 1024;
/* temp1 = P( t ).B`( t ) */
/* temp1 = P( t ).B'( t ) */
temp1 = VEC_26D6_DOT( dist_vector, d1 );
/* temp2 = ( B`( t ).B`( t ) + P( t ).B``( t ) ) */
/* temp2 = ( B'( t ).B'( t ) + P( t ).B''( t ) ) */
temp2 = VEC_26D6_DOT( d1, d1 ) +
VEC_26D6_DOT( dist_vector, d2 );
@ -1595,7 +1595,7 @@
}
}
/* B`( t ) = 2tA + B */
/* B'( t ) = 2tA + B */
direction.x = 2 * FT_MulFix( aA.x, min_factor ) + bB.x;
direction.y = 2 * FT_MulFix( aA.y, min_factor ) + bB.y;
@ -1670,10 +1670,10 @@
/* B( t ) = t^3( A ) + t^2( B ) + tC + p0 */
/* */
/* => the derivative of the above equation is written as */
/* B`( t ) = 3t^2( A ) + 2t( B ) + C */
/* B'( t ) = 3t^2( A ) + 2t( B ) + C */
/* */
/* => further derivative of the above equation is written as */
/* B``( t ) = 6t( A ) + 2B */
/* B''( t ) = 6t( A ) + 2B */
/* */
/* => the equation of distance from point `p' to the curve */
/* P( t ) can be written as */
@ -1683,7 +1683,7 @@
/* */
/* => finally the equation of angle between curve B( t ) and */
/* point to curve distance P( t ) can be written as */
/* Q( t ) = P( t ).B`( t ) */
/* Q( t ) = P( t ).B'( t ) */
/* */
/* => now our task is to find a value of t such that the above */
/* equation Q( t ) becomes zero. in other words the point */
@ -1693,19 +1693,19 @@
/* => we first assume a arbitary value of the factor `t' and */
/* then we improve it using Newton's equation such as */
/* */
/* t -= Q( t ) / Q`( t ) */
/* t -= Q( t ) / Q'( t ) */
/* putting value of Q( t ) from the above equation gives */
/* */
/* t -= P( t ).B`( t ) / derivative( P( t ).B`( t ) ) */
/* t -= P( t ).B`( t ) / */
/* ( P`( t )B`( t ) + P( t ).B``( t ) ) */
/* t -= P( t ).B'( t ) / derivative( P( t ).B'( t ) ) */
/* t -= P( t ).B'( t ) / */
/* ( P'( t )B'( t ) + P( t ).B''( t ) ) */
/* */
/* P`( t ) is noting but B`( t ) because the constant are */
/* P'( t ) is noting but B'( t ) because the constant are */
/* gone due to derivative */
/* */
/* => finally we get the equation to improve the factor as */
/* t -= P( t ).B`( t ) / */
/* ( B`( t ).B`( t ) + P( t ).B``( t ) ) */
/* t -= P( t ).B'( t ) / */
/* ( B'( t ).B'( t ) + P( t ).B''( t ) ) */
/* */
/* [note]: B and B( t ) are different in the above equations */
@ -1809,26 +1809,26 @@
}
/* This the actual Newton's approximation. */
/* t -= P( t ).B`( t ) / */
/* ( B`( t ).B`( t ) + P( t ).B``( t ) ) */
/* t -= P( t ).B'( t ) / */
/* ( B'( t ).B'( t ) + P( t ).B''( t ) ) */
/* B`( t ) = 3t^2( A ) + 2t( B ) + C */
/* B'( t ) = 3t^2( A ) + 2t( B ) + C */
d1.x = FT_MulFix( aA.x, 3 * factor2 ) +
FT_MulFix( bB.x, 2 * factor ) + cC.x;
d1.y = FT_MulFix( aA.y, 3 * factor2 ) +
FT_MulFix( bB.y, 2 * factor ) + cC.y;
/* B``( t ) = 6t( A ) + 2B */
/* B''( t ) = 6t( A ) + 2B */
d2.x = FT_MulFix( aA.x, 6 * factor ) + 2 * bB.x;
d2.y = FT_MulFix( aA.y, 6 * factor ) + 2 * bB.y;
dist_vector.x /= 1024;
dist_vector.y /= 1024;
/* temp1 = P( t ).B`( t ) */
/* temp1 = P( t ).B'( t ) */
temp1 = VEC_26D6_DOT( dist_vector, d1 );
/* temp2 = ( B`( t ).B`( t ) + P( t ).B``( t ) ) */
/* temp2 = ( B'( t ).B'( t ) + P( t ).B''( t ) ) */
temp2 = VEC_26D6_DOT( d1, d1 ) +
VEC_26D6_DOT( dist_vector, d2 );
@ -1839,7 +1839,7 @@
}
}
/* B`( t ) = 3t^2( A ) + 2t( B ) + C */
/* B'( t ) = 3t^2( A ) + 2t( B ) + C */
direction.x = FT_MulFix( aA.x, 3 * min_factor_sq ) +
FT_MulFix( bB.x, 2 * min_factor ) + cC.x;
direction.y = FT_MulFix( aA.y, 3 * min_factor_sq ) +