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There are two types of arbitrary quadrangle transformations, Perspective and Bilinear. The image transformer always uses reverse transformations, and there is a problem. The Perspective transformations are perfectly reversible, so they work correctly with images, but the Bilinear transformer behave somehow strange. It can transform a rectangle to a quadrangle, but not vice versa. In this example you can see this effect, when the edges of the image "sag". I'd highly appreciate if someone could help me with math for transformations similar to Bilinear ones, but correctly reversible (i.e., that can transform an arbitrary quadrangle to a rectangle). The bilinear transformations are simple, see agg_trans_bilinear.h and agg_simul_eq.h Note: F2 key saves current "screenshot" file in this demo's directory. v8AGG Example. Image Perspective Transformations (F1-Help)spheresvlspheresvmFile not found: %s$m'%s. Download http://www.antigrain.com/Xm%shm2%s or copy it from another directory if available.mFile not found: %sm%sthe_applicationfimage_perspective-DT! @$0123456789abcdef0123456789ABCDEFt&f@ 0.- agg_types int8_type int8u_type int16_type int16u_type int32_type int32u_type int64_type int64u_typeint8_ptr int8u_ptr int16_ptr int16u_ptr int32_ptr int32u_ptr int64_ptr int64u_ptr int8u_ptr_ptrint_ptrv unsigned_ptr int8u_01_ptrByte int8u_01o int16u_oovSmallInt int32_oo int32_int8uoooovWord int32u_HpHpvp32_ptrvPointervLongInt p32ppvdouble_ptr_ptr double_ptr double_2_ptrDoublev double_2p double_8_ptr double_8p double_42_ptr p double_42Xq double_44_ptr p double_44 q double_81_ptr p double_81q double_88_ptr p double_88@r double_26_ptr double_26p double_00_ptrDoublev double_00r double_00p char_ptr_ptrchar_ptr pointer_ptrvrect_ptrrectn agg_basicsv rect_d_ptrrect_dn agg_basicspoint_type_ptr point_typepp vertex_type$n agg_basicstSCAN#SCAN_0SCAN_1SCAN_2SCAN_3SCAN_4SCAN_5SCAN_6SCAN_7SCAN_8SCAN_9SCAN_ASCAN_BSCAN_CSCAN_DSCAN_ESCAN_FSCAN_GSCAN_HSCAN_ISCAN_JSCAN_KSCAN_LSCAN_MSCAN_NSCAN_OSCAN_PSCAN_QSCAN_RSCAN_SSCAN_TSCAN_USCAN_VSCAN_WSCAN_XSCAN_YSCAN_ZvtITEM#ITEM_0ITEM_1ITEM_2ITEM_3ITEM_4ITEM_5ITEM_6ITEM_7ITEM_8ITEM_9ITEM_AITEM_BITEM_CITEM_DITEM_EITEM_FITEM_GITEM_HITEM_IITEM_JITEM_KITEM_LITEM_MITEM_NITEM_OITEM_PITEM_QITEM_RITEM_SITEM_TITEM_UITEM_VITEM_WITEM_XITEM_YITEM_Zvscan_string_flags_width _precision_prefix_type M,<\l  Anti-Grain Geometry Applicationvppm/vv vP6 v 255 vUnable to open DISPLAY!w;There's no Visual compatible with minimal AGG requirements:Pw;At least 15-bit color depth and True- or DirectColor class.w4RGB masks are not compatible with AGG pixel formats:vwR=wG=wB= xWM_DELETE_WINDOWvscreenshot.ppm.ppm?Lx/ PRESS ANY KEY TO CONTINUE THE AGGPAS DEMO ...x/ PRESS ANY KEY TO CONTINUE THE AGGPAS DEMO ...x/ PRESS ANY KEY TO CONTINUE THE AGGPAS DEMO ...y/ PRESS ANY KEY TO CONTINUE THE AGGPAS DEMO ...=n?+ @= ףp= ? ףp= ף?@@ @image_filter_base_ptrimage_filter_baseagg_image_filtersvimage_filter_lut_ptrimage_filter_lutagg_image_filtersimage_filter_ptr image_filteragg_image_filtersimage_filter_bilinear_ptrimage_filter_bilinearagg_image_filtersvimage_filter_hanning_ptrimage_filter_hanningؙagg_image_filtersimage_filter_hamming_ptrimage_filter_hammingagg_image_filtersimage_filter_hermite_ptrimage_filter_hermiteagg_image_filtersimage_filter_quadric_ptrimage_filter_quadric,agg_image_filtersimage_filter_bicubic_ptrimage_filter_bicubicHagg_image_filtersimage_filter_kaiser_ptrvimage_filter_kaiserdagg_image_filtersimage_filter_catrom_ptrvimage_filter_catromagg_image_filtersimage_filter_mitchell_ptrimage_filter_mitchellagg_image_filtersvimage_filter_spline16_ptrimage_filter_spline16agg_image_filtersvimage_filter_spline36_ptrimage_filter_spline36Ԛagg_image_filtersvimage_filter_gaussian_ptrimage_filter_gaussianagg_image_filtersvimage_filter_bessel_ptrvimage_filter_bessel agg_image_filtersimage_filter_sinc_ptrimage_filter_sinc(agg_image_filtersvimage_filter_lanczos_ptrimage_filter_lanczosDagg_image_filtersimage_filter_blackman_ptrimage_filter_blackman`agg_image_filtersvimage_filter_sinc36_ptrvimage_filter_sinc36|agg_image_filtersimage_filter_sinc64_ptrvimage_filter_sinc64agg_image_filtersimage_filter_sinc100_ptrimage_filter_sinc100agg_image_filtersimage_filter_sinc144_ptrimage_filter_sinc144Лagg_image_filtersimage_filter_sinc196_ptrimage_filter_sinc196agg_image_filtersimage_filter_sinc256_ptrimage_filter_sinc256agg_image_filtersimage_filter_lanczos36_ptrimage_filter_lanczos36$agg_image_filtersimage_filter_lanczos64_ptrimage_filter_lanczos64@agg_image_filtersimage_filter_lanczos100_ptrvimage_filter_lanczos100\agg_image_filtersimage_filter_lanczos144_ptrvimage_filter_lanczos144xagg_image_filtersimage_filter_lanczos196_ptrvimage_filter_lanczos196agg_image_filtersimage_filter_lanczos256_ptrvimage_filter_lanczos256agg_image_filtersimage_filter_blackman36_ptrvimage_filter_blackman36̜agg_image_filtersimage_filter_blackman64_ptrvimage_filter_blackman64agg_image_filtersimage_filter_blackman100_ptrimage_filter_blackman100agg_image_filtersimage_filter_blackman144_ptrimage_filter_blackman144 agg_image_filtersimage_filter_blackman196_ptrimage_filter_blackman196<agg_image_filtersimage_filter_blackman256_ptrimage_filter_blackman256Xagg_image_filtersx L\l| L\l @l Font (c) MicroProf 27 Septemb.1989 4F.>d8Dh$@HRZ&Lj| D^(6HN`nt,<h|2Td> H   & 4 J f p ~  " 2 V ` n |  0 V r  & 6 B N \ x &Hd&<Xlllllllllllllllllrzzz zzz d dcc~~~~~~~~|~k~~~~~~~{}~~~}}y~~u~~~ ~}|{|{|}~|}{|{}|~}|{|{|}~|}{|{}| t zz n~~ }{}{} k ~~~}v x}~}~ rkw~}~}~}{{|~~}k~~~~~}~ }~~|{{}~~wwww~~~~} }}~~}}~x~~~}}}~~x~ kk k ~~~ ~}~~~}{}~~k~~}{}~~k  k ~~}{}~~kkk p}kr tk kkkkkkk ~~}{}~~ k ~}~ ~~}{}~~zk ~~~u~~~~~}~kq}~kk kkkkkkvuv kllhll{|~~r~}~}~k~}~}~~}~}~k~}~}~ ~}~}~ }op} ~}~}~k}vro} k vxkr}v}vr}v~}~}~ k~}~}~k~}~}~r~~~~o}v}rrrrrrr rrrr|~r  ~~~~~~~~~~~~~~~~~~~~~~~~~~ww~~~~~~~~~~~~~~~~~~~~~~~~~~ }}k k  ~~}~ ~~}} ~ k} v vu }{~}z~k kk k v uk k k k~|y|} k }{~~|y{~ k wz z ~~u~k kk}ku} kkk kk }k kk }p~ }p~ }y~  ~t|~~w~ ~{~~x~ }~}~} ~w~  ~}{|w qyy~}}~}~s~ ~s~ ~x qw q  ~}{| ~}v ~v k ~}{|~}v~}vt~n~ ~~t k  qs~ ~~y~qs~ ~ ~s~ ~ ~~q q qq ~u~~u~ ~{~ t&$@statusinitial next_char start_glyphglyph gsv_text_ptrgsv_text8 agg_gsv_textgsv_text_outlined agg_gsv_text,L\lXL\l̹ t&??BzՔ?simple_polygon_vertex_sourceinteractive_polygon_interactive_polygoninteractive_polygon_  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`ABCDEFGHIJKLMNOPQRSTUVWXYZ{|}~/.tSCAN#SCAN_0SCAN_1SCAN_2SCAN_3SCAN_4SCAN_5SCAN_6SCAN_7SCAN_8SCAN_9SCAN_ASCAN_BSCAN_CSCAN_DSCAN_ESCAN_FSCAN_GSCAN_HSCAN_ISCAN_JSCAN_KSCAN_LSCAN_MSCAN_NSCAN_OSCAN_PSCAN_QSCAN_RSCAN_SSCAN_TSCAN_USCAN_VSCAN_WSCAN_XSCAN_YSCAN_ZvtITEM#ITEM_0ITEM_1ITEM_2ITEM_3ITEM_4ITEM_5ITEM_6ITEM_7ITEM_8ITEM_9ITEM_AITEM_BITEM_CITEM_DITEM_EITEM_FITEM_GITEM_HITEM_IITEM_JITEM_KITEM_LITEM_MITEM_NITEM_OITEM_PITEM_QITEM_RITEM_SITEM_TITEM_UITEM_VITEM_WITEM_XITEM_YITEM_Z(Ԑ<t&KH9t&??aspect_ratio_easpect_ratio_stretchaspect_ratio_meetaspect_ratio_slicetrans_viewport_ptrtrans_viewport(agg_trans_viewportCopyRow,L\lt&vertex_source_ptr vertex_sourceagg_vertex_sourceؠؠؠ,,<\,(,  func_lessarray_base_ptr array_base agg_arraypod_array_adaptor_ptrpod_array_adaptor agg_arrayvpod_auto_array_ptrpod_auto_array agg_array pod_array agg_arrayv pod_deque_ptr pod_deque agg_arrayv pod_alloc_ptrLongWord pod_allocnT pod_allocator agg_arrayv int80_ptrLongInt int80P,L\l,L\lL,L\l,L\lL ,L\l t&t&? gamma_noneagg_gamma_functions gamma_poweragg_gamma_functionsvgamma_thresholdDagg_gamma_functionsv gamma_linearpagg_gamma_functionsgamma_multiplyagg_gamma_functionst&KHKH9KHKH9KHKH9KHKH9  lLlؠؠ span_p8_ptrvSmallInt span_p8ppnvscanline_p8_ptrv scanline_p8agg_scanline_p|<ؠ,L|ؠؠ span_bin_ptrSmallInt span_binHH scanline_binagg_scanline_bin,L\l<ؠt&span_generator_ptrspan_generatoragg_span_generator9,L\llt&t&@?@ ellipse_ptrvellipse, agg_ellipseKH9P *L !"#$%^&1'(()U*++,A--.T/00Q112:33v455B66m788"99>::T;;f<>?@@@|AAtBBiCCZDDHEE3FFGGHqHHRII0JJ KyKKQLL&MMMbNN2OOPfPP1QQQ]RR#SSSITT UkUU*VVVEWWX]XXYqYY(ZZZ7[[[C\\\L]]]R^^^U__`U```SaaaNbbbGccc=ddd1eee#fsffgbgghOhhh9iii"jojjkUkkk9lllmfmmmFnnn$omoopIppp#qkqqqCrrrsasss5t{ttuNuuuvdvvv3wwwwxDxxxySyyyz`zzz){k{{{2|s|||8}z}}}=~~~~~?@>~;z6t/l&cޅX҆Kćldz"P}ش2_AnǶ!Nzӷ-Y޸ 7c?kúFrʻ!Lxϼ%Q|ҽ(S~Ծ*Uտ+U*T(R|¦$NxâIsĜClŖſ;eƎƷ 3\DžǮ)R{ȤGoɘ:cʋʴ-U}˦Fn̖̾6^͆ͮ%MuΜ;bϊϱ'OvН:aшѯ%Lrҙ5\ӂөDjԑԷ+Qw՞7]փ֪Bh׎״&Lrؗؽ /Tz٠6\ځڧ_ @`t&?ư>@@3333333?N@@KH9@ double_xy_ptrDoublev double_xyPP poly_xy_ptrv poly_xy\vstorage_xy_ptrLongWord storage_xyt&?@@@d9;;l ==t&t&?@)\(??@status_e initialreadycap1cap2outline1 close_firstoutline2 out_vertices end_poly1 end_poly2stopvcgen_stroke_ptr vcgen_stroke,agg_vcgen_stroke,LD|DlDE0,L\lFFnull_markers_ptr null_markersLagg_conv_adaptor_vcgenvstatusinitial accumulategenerateconv_adaptor_vcgen_ptrconv_adaptor_vcgenxagg_conv_adaptor_vcgen,,+=func_vertex_sequencevertex_sequence_ptrvvertex_sequencetagg_vertex_sequencevvertex_dist_ptrvDoublev vertex_distvvertex_dist_cmd_ptrvLongWord vertex_dist_cmd lؠؠؠؠؠؠؠؠOOOPRSUVOOOPRSUVOOOPRSUVOOOPRSUVOOOPRSUVOOOPRSUVOOOPRSUVOOOPRSUVOOOPRSUVOOOPRSUVOOOPRSUVOOOPRSUVOOOPRSUVOOOPRSUVOOOPRSUVOOOPRSUVOOOPRSUVOOOPRSUVOOOPRSUVOOOPRSUVOOOPRSUVOOOPRSUVOOOPRSUVOOOPRSUVOOOPRSUVOOOPRSUVOOOPRSUVOOOPRSUVOOOPRSUVOOOPRSUVbbblc dd|e,fbbblc dd|e,fbbblc dd|e,fbbblc dd|e,fbbblc dd|e,fbbblc dd|e,fbbblc dd|e,fbbblc dd|e,fbbblc dd|e,fbbblc dd|e,fbbblc dd|e,fbbblc dd|e,fbbblc dd|e,fbbblc dd|e,fbbblc dd|e,fbbblc dd|e,fbbblc dd|e,fbbblc dd|e,fbbblc dd|e,fbbblc dd|e,fbbblc dd|e,fbbblc dd|e,fbbblc dd|e,fbbblc dd|e,fbbblc dd|e,fbbblc dd|e,fbbblc dd|e,fbbblc dd|e,fbbblc dd|e,fbbblc dd|e,ffunc_mask_calculatevalpha_mask_ptr alpha_maskagg_alpha_mask_u8 alpha_mask_u8agg_alpha_mask_u8valpha_mask_gray8 agg_alpha_mask_u8alpha_mask_rgb24rPagg_alpha_mask_u8valpha_mask_rgb24gagg_alpha_mask_u8valpha_mask_rgb24bagg_alpha_mask_u8valpha_mask_bgr24ragg_alpha_mask_u8valpha_mask_bgr24gagg_alpha_mask_u8valpha_mask_bgr24b@agg_alpha_mask_u8valpha_mask_rgba32rpagg_alpha_mask_u8alpha_mask_rgba32gagg_alpha_mask_u8alpha_mask_rgba32bagg_alpha_mask_u8alpha_mask_rgba32aagg_alpha_mask_u8alpha_mask_argb32r0agg_alpha_mask_u8alpha_mask_argb32g`agg_alpha_mask_u8alpha_mask_argb32bagg_alpha_mask_u8alpha_mask_argb32aagg_alpha_mask_u8alpha_mask_bgra32ragg_alpha_mask_u8alpha_mask_bgra32g agg_alpha_mask_u8alpha_mask_bgra32bPagg_alpha_mask_u8alpha_mask_bgra32aagg_alpha_mask_u8alpha_mask_abgr32ragg_alpha_mask_u8alpha_mask_abgr32gagg_alpha_mask_u8alpha_mask_abgr32bagg_alpha_mask_u8alpha_mask_abgr32a@agg_alpha_mask_u8alpha_mask_rgb24graypagg_alpha_mask_u8alpha_mask_bgr24grayagg_alpha_mask_u8alpha_mask_rgba32grayagg_alpha_mask_u8valpha_mask_argb32grayagg_alpha_mask_u8valpha_mask_bgra32gray0agg_alpha_mask_u8valpha_mask_abgr32gray`agg_alpha_mask_u8vamask_no_clip_u8agg_alpha_mask_u8amask_no_clip_gray8agg_alpha_mask_u8amask_no_clip_rgb24ragg_alpha_mask_u8amask_no_clip_rgb24g agg_alpha_mask_u8amask_no_clip_rgb24bPagg_alpha_mask_u8amask_no_clip_bgr24ragg_alpha_mask_u8amask_no_clip_bgr24gagg_alpha_mask_u8amask_no_clip_bgr24bagg_alpha_mask_u8amask_no_clip_rgba32ragg_alpha_mask_u8vamask_no_clip_rgba32g@agg_alpha_mask_u8vamask_no_clip_rgba32bpagg_alpha_mask_u8vamask_no_clip_rgba32aagg_alpha_mask_u8vamask_no_clip_argb32ragg_alpha_mask_u8vamask_no_clip_argb32gagg_alpha_mask_u8vamask_no_clip_argb32b0agg_alpha_mask_u8vamask_no_clip_argb32a`agg_alpha_mask_u8vamask_no_clip_bgra32ragg_alpha_mask_u8vamask_no_clip_bgra32gagg_alpha_mask_u8vamask_no_clip_bgra32bagg_alpha_mask_u8vamask_no_clip_bgra32a agg_alpha_mask_u8vamask_no_clip_abgr32rPagg_alpha_mask_u8vamask_no_clip_abgr32gagg_alpha_mask_u8vamask_no_clip_abgr32bagg_alpha_mask_u8vamask_no_clip_abgr32aagg_alpha_mask_u8vamask_no_clip_rgb24grayagg_alpha_mask_u8amask_no_clip_bgr24gray@agg_alpha_mask_u8amask_no_clip_rgba32graypagg_alpha_mask_u8amask_no_clip_argb32grayagg_alpha_mask_u8amask_no_clip_bgra32grayagg_alpha_mask_u8amask_no_clip_abgr32grayagg_alpha_mask_u8,L\ltt,L\lttt&@@@?? 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