how can i find the intersection point between the vertical lines and the curve (xmin,ymin) ?

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Hi, i want to find the intersection point between the green vertical lines and the red curve (xmin,ymin) and display the point coordinates,
if there is another declaration to vertical line please tell me and thank you
this is my script :
clc,clear all
x=[900 899.5 899 898.5 898 897.5 897 896.5 896 895.5 895 894.5 894 893.5 893 892.5 892 891.5 891 890.5 890 889.5 889 888.5 888 887.5 887 886.5 886 885.5 885 884.5 884 883.5 883 882.5 882 881.5 881 880.5 880 879.5 879 878.5 878 877.5 877 876.5 876 875.5 875 874.5 874 873.5 873 872.5 872 871.5 871 870.5 870 869.5 869 868.5 868 867.5 867 866.5 866 865.5 865 864.5 864 863.5 863 862.5 862 861.5 861 860.5 860 859.5 859 858.5 858 857.5 857 856.5 856 855.5 855 854.5 854 853.5 853 852.5 852 851.5 851 850.5 850 849.5 849 848.5 848 847.5 847 846.5 846 845.5 845 844.5 844 843.5 843 842.5 842 841.5 841 840.5 840 839.5 839 838.5 838 837.5 837 836.5 836 835.5 835 834.5 834 833.5 833 832.5 832 831.5 831 830.5 830 829.5 829 828.5 828 827.5 827 826.5 826 825.5 825 824.5 824 823.5 823 822.5 822 821.5 821 820.5 820 819.5 819 818.5 818 817.5 817 816.5 816 815.5 815 814.5 814 813.5 813 812.5 812 811.5 811 810.5 810 809.5 809 808.5 808 807.5 807 806.5 806 805.5 805 804.5 804 803.5 803 802.5 802 801.5 801 800.5 800 799.5 799 798.5 798 797.5 797 796.5 796 795.5 795 794.5 794 793.5 793 792.5 792 791.5 791 790.5 790 789.5 789 788.5 788 787.5 787 786.5 786 785.5 785 784.5 784 783.5 783 782.5 782 781.5 781 780.5 780 779.5 779 778.5 778 777.5 777 776.5 776 775.5 775 774.5 774 773.5 773 772.5 772 771.5 771 770.5 770 769.5 769 768.5 768 767.5 767 766.5 766 765.5 765 764.5 764 763.5 763 762.5 762 761.5 761 760.5 760 759.5 759 758.5 758 757.5 757 756.5 756 755.5 755 754.5 754 753.5 753 752.5 752 751.5 751 750.5 750 749.5 749 748.5 748 747.5 747 746.5 746 745.5 745 744.5 744 743.5 743 742.5 742 741.5 741 740.5 740 739.5 739 738.5 738 737.5 737 736.5 736 735.5 735 734.5 734 733.5 733 732.5 732 731.5 731 730.5 730 729.5 729 728.5 728 727.5 727 726.5 726 725.5 725 724.5 724 723.5 723 722.5 722 721.5 721 720.5 720 719.5 719 718.5 718 717.5 717 716.5 716 715.5 715 714.5 714 713.5 713 712.5 712 711.5 711 710.5 710 709.5 709 708.5 708 707.5 707 706.5 706 705.5 705 704.5 704 703.5 703 702.5 702 701.5 701 700.5 700 699.5 699 698.5 698 697.5 697 696.5 696 695.5 695 694.5 694 693.5 693 692.5 692 691.5 691 690.5 690 689.5 689 688.5 688 687.5 687 686.5 686 685.5 685 684.5 684 683.5 683 682.5 682 681.5 681 680.5 680 679.5 679 678.5 678 677.5 677 676.5 676 675.5 675 674.5 674 673.5 673 672.5 672 671.5 671 670.5 670 669.5 669 668.5 668 667.5 667 666.5 666 665.5 665 664.5 664 663.5 663 662.5 662 661.5 661 660.5 660 659.5 659 658.5 658 657.5 657 656.5 656 655.5 655 654.5 654 653.5 653 652.5 652 651.5 651 650.5 650 649.5 649 648.5 648 647.5 647 646.5 646 645.5 645 644.5 644 643.5 643 642.5 642 641.5 641 640.5 640 639.5 639 638.5 638 637.5 637 636.5 636 635.5 635 634.5 634 633.5 633 632.5 632 631.5 631 630.5 630 629.5 629 628.5 628 627.5 627 626.5 626 625.5 625 624.5 624 623.5 623 622.5 622 621.5 621 620.5 620 619.5 619 618.5 618 617.5 617 616.5 616 615.5 615 614.5 614 613.5 613 612.5 612 611.5 611 610.5 610 609.5 609 608.5 608 607.5 607 606.5 606 605.5 605 604.5 604 603.5 603 602.5 602 601.5 601 600.5 600 599.5 599 598.5 598 597.5 597 596.5 596 595.5 595 594.5 594 593.5 593 592.5 592 591.5 591 590.5 590 589.5 589 588.5 588 587.5 587 586.5 586 585.5 585 584.5 584 583.5 583 582.5 582 581.5 581 580.5 580 579.5 579 578.5 578 577.5 577 576.5 576 575.5 575 574.5 574 573.5 573 572.5 572 571.5 571 570.5 570 569.5 569 568.5 568 567.5 567 566.5 566 565.5 565 564.5 564 563.5 563 562.5 562 561.5 561 560.5 560 559.5 559 558.5 558 557.5 557 556.5 556 555.5 555 554.5 554 553.5 553 552.5 552 551.5 551 550.5 550 549.5 549 548.5 548 547.5 547 546.5 546 545.5 545 544.5 544 543.5 543 542.5 542 541.5 541 540.5 540 539.5 539 538.5 538 537.5 537 536.5 536 535.5 535 534.5 534 533.5 533 532.5 532 531.5 531 530.5 530 529.5 529 528.5 528 527.5 527 526.5 526 525.5 525 524.5 524 523.5 523 522.5 522 521.5 521 520.5 520 519.5 519 518.5 518 517.5 517 516.5 516 515.5 515 514.5 514 513.5 513 512.5 512 511.5 511 510.5 510 509.5 509 508.5 508 507.5 507 506.5 506 505.5 505 504.5 504 503.5 503 502.5 502 501.5 501 500.5 500 499.5 499 498.5 498 497.5 497 496.5 496 495.5 495 494.5 494 493.5 493 492.5 492 491.5 491 490.5 490 489.5 489 488.5 488 487.5 487 486.5 486 485.5 485 484.5 484 483.5 483 482.5 482 481.5 481 480.5 480 479.5 479 478.5 478 477.5 477 476.5 476 475.5 475 474.5 474 473.5 473 472.5 472 471.5 471 470.5 470 469.5 469 468.5 468 467.5 467 466.5 466 465.5 465 464.5 464 463.5 463 462.5 462 461.5 461 460.5 460 459.5 459 458.5 458 457.5 457 456.5 456 455.5 455 454.5 454 453.5 453 452.5 452 451.5 451 450.5 450 449.5 449 448.5 448 447.5 447 446.5 446 445.5 445 444.5 444 443.5 443 442.5 442 441.5 441 440.5 440 439.5 439 438.5 438 437.5 437 436.5 436 435.5 435 434.5 434 433.5 433 432.5 432 431.5 431 430.5 430 429.5 429 428.5 428 427.5 427 426.5 426 425.5 425 424.5 424 423.5 423 422.5 422 421.5 421 420.5 420 419.5 419 418.5 418 417.5 417 416.5 416 415.5 415 414.5 414 413.5 413 412.5 412 411.5 411 410.5 410 409.5 409 408.5 408 407.5 407 406.5 406 405.5 405 404.5 404 403.5 403 402.5 402 401.5 401 400.5 400 399.5 399 398.5 398 397.5 397 396.5 396 395.5 395 394.5 394 393.5 393 392.5 392 391.5 391 390.5 390 389.5 389 388.5 388 387.5 387 386.5 386 385.5 385 384.5 384 383.5 383 382.5 382 381.5 381 380.5 380 379.5 379 378.5 378 377.5 377 376.5 376 375.5 375 374.5 374 373.5 373 372.5 372 371.5 371 370.5 370 369.5 369 368.5 368 367.5 367 366.5 366 365.5 365 364.5 364 363.5 363 362.5 362 361.5 361 360.5 360 359.5 359 358.5 358 357.5 357 356.5 356 355.5 355 354.5 354 353.5 353 352.5 352 351.5 351 350.5 350 349.5 349 348.5 348 347.5 347 346.5 346 345.5 345 344.5 344 343.5 343 342.5 342 341.5 341 340.5 340 339.5 339 338.5 338 337.5 337 336.5 336 335.5 335 334.5 334 333.5 333 332.5 332 331.5 331 330.5 330 329.5 329 328.5 328 327.5 327 326.5 326 325.5 325 324.5 324 323.5 323 322.5 322 321.5 321 320.5 320 319.5 319 318.5 318 317.5 317 316.5 316 315.5 315 314.5 314 313.5 313 312.5 312 311.5 311 310.5 310 309.5 309 308.5 308 307.5 307 306.5 306 305.5 305 304.5 304 303.5 303 302.5 302 301.5 301 300.5 300 299.5 299 298.5 298 297.5 297 296.5 296 295.5 295 294.5 294 293.5 293 292.5 292 291.5 291 290.5 290];
y=[81.111 81.076 81.041 81.017 80.985 80.96 80.942 80.91 80.866 80.841 80.832 80.805 80.767 80.734 80.718 80.686 80.654 80.626 80.599 80.573 80.553 80.541 80.529 80.495 80.458 80.443 80.426 80.4 80.382 80.356 80.318 80.29 80.281 80.254 80.242 80.228 80.214 80.181 80.152 80.127 80.113 80.092 80.075 80.055 80.037 80.008 79.99 79.97 79.95 79.936 79.918 79.915 79.901 79.883 79.865 79.846 79.83 79.811 79.792 79.773 79.761 79.766 79.752 79.732 79.721 79.691 79.676 79.672 79.669 79.657 79.636 79.627 79.616 79.599 79.579 79.567 79.569 79.566 79.547 79.532 79.529 79.517 79.517 79.505 79.499 79.492 79.488 79.491 79.494 79.483 79.463 79.454 79.448 79.453 79.436 79.438 79.447 79.439 79.428 79.427 79.433 79.438 79.438 79.43 79.419 79.422 79.421 79.425 79.427 79.415 79.421 79.433 79.424 79.421 79.421 79.424 79.434 79.445 79.444 79.434 79.439 79.441 79.451 79.46 79.459 79.456 79.463 79.48 79.503 79.511 79.52 79.526 79.524 79.535 79.54 79.54 79.546 79.575 79.599 79.608 79.622 79.637 79.634 79.64 79.648 79.659 79.679 79.689 79.709 79.717 79.737 79.758 79.776 79.782 79.796 79.814 79.824 79.842 79.865 79.883 79.897 79.921 79.944 79.958 79.976 79.993 80.017 80.039 80.06 80.072 80.101 80.112 80.133 80.162 80.182 80.222 80.239 80.266 80.28 80.3 80.323 80.347 80.38 80.409 80.426 80.452 80.469 80.506 80.536 80.556 80.574 80.606 80.632 80.666 80.702 80.728 80.754 80.78 80.811 80.837 80.866 80.895 80.928 80.963 81.002 81.027 81.041 81.078 81.108 81.136 81.16 81.191 81.227 81.261 81.302 81.333 81.371 81.392 81.426 81.459 81.499 81.526 81.554 81.587 81.624 81.656 81.7 81.726 81.755 81.797 81.842 81.874 81.909 81.96 81.995 82.021 82.041 82.074 82.118 82.169 82.201 82.227 82.25 82.288 82.331 82.369 82.399 82.436 82.474 82.515 82.544 82.587 82.628 82.663 82.686 82.727 82.758 82.791 82.836 82.875 82.906 82.939 82.967 83.011 83.061 83.089 83.122 83.17 83.202 83.24 83.269 83.293 83.33 83.376 83.411 83.451 83.489 83.516 83.539 83.573 83.612 83.644 83.673 83.71 83.753 83.782 83.809 83.838 83.875 83.892 83.911 83.957 83.991 84.024 84.055 84.075 84.102 84.142 84.166 84.194 84.223 84.259 84.276 84.3 84.336 84.363 84.386 84.41 84.442 84.467 84.485 84.502 84.52 84.549 84.59 84.615 84.633 84.648 84.673 84.694 84.712 84.734 84.766 84.78 84.792 84.81 84.83 84.85 84.87 84.879 84.896 84.908 84.917 84.931 84.946 84.961 84.978 84.999 84.996 85.01 85.027 85.044 85.056 85.059 85.05 85.068 85.073 85.083 85.082 85.089 85.085 85.091 85.094 85.108 85.103 85.1 85.106 85.106 85.099 85.108 85.106 85.099 85.089 85.086 85.091 85.085 85.076 85.066 85.062 85.06 85.053 85.041 85.025 85.018 85.007 84.989 84.979 84.97 84.952 84.943 84.918 84.908 84.905 84.888 84.86 84.845 84.827 84.793 84.777 84.758 84.732 84.717 84.69 84.662 84.642 84.612 84.58 84.552 84.52 84.497 84.482 84.433 84.397 84.362 84.334 84.311 84.285 84.244 84.203 84.175 84.148 84.099 84.061 84.02 83.994 83.953 83.913 83.861 83.829 83.792 83.75 83.71 83.679 83.632 83.586 83.542 83.499 83.444 83.408 83.365 83.328 83.274 83.222 83.168 83.127 83.084 83.04 82.985 82.933 82.888 82.836 82.784 82.729 82.677 82.63 82.576 82.524 82.46 82.414 82.36 82.303 82.253 82.204 82.134 82.074 82.022 81.967 81.917 81.859 81.798 81.746 81.694 81.632 81.571 81.519 81.468 81.409 81.349 81.291 81.229 81.168 81.111 81.06 81.002 80.939 80.884 80.831 80.774 80.718 80.66 80.594 80.533 80.475 80.419 80.365 80.309 80.257 80.2 80.144 80.088 80.03 79.973 79.926 79.875 79.816 79.753 79.7 79.653 79.592 79.526 79.482 79.427 79.381 79.332 79.28 79.218 79.177 79.134 79.091 79.047 79 78.954 78.903 78.861 78.812 78.768 78.722 78.687 78.644 78.583 78.543 78.516 78.476 78.437 78.397 78.356 78.322 78.281 78.238 78.195 78.148 78.104 78.061 78.028 77.991 77.959 77.935 77.907 77.877 77.861 77.829 77.799 77.779 77.741 77.71 77.683 77.652 77.631 77.613 77.585 77.565 77.547 77.526 77.509 77.475 77.448 77.423 77.416 77.413 77.402 77.385 77.376 77.359 77.346 77.336 77.32 77.31 77.312 77.306 77.292 77.291 77.289 77.286 77.283 77.281 77.292 77.283 77.277 77.274 77.291 77.304 77.303 77.298 77.292 77.292 77.304 77.326 77.332 77.338 77.355 77.364 77.376 77.385 77.404 77.414 77.428 77.443 77.457 77.474 77.489 77.51 77.538 77.559 77.587 77.603 77.617 77.642 77.666 77.693 77.722 77.744 77.765 77.793 77.814 77.835 77.863 77.901 77.924 77.956 77.98 78.006 78.034 78.064 78.105 78.137 78.168 78.211 78.243 78.273 78.307 78.337 78.369 78.403 78.438 78.476 78.504 78.552 78.588 78.615 78.653 78.696 78.719 78.762 78.794 78.82 78.852 78.882 78.923 78.968 78.997 79.027 79.058 79.093 79.131 79.158 79.193 79.225 79.254 79.286 79.315 79.332 79.36 79.398 79.427 79.451 79.488 79.511 79.546 79.567 79.589 79.615 79.639 79.65 79.666 79.686 79.703 79.721 79.75 79.784 79.799 79.808 79.819 79.822 79.833 79.849 79.86 79.868 79.891 79.897 79.912 79.918 79.914 79.915 79.917 79.918 79.935 79.93 79.915 79.911 79.904 79.891 79.891 79.877 79.869 79.859 79.845 79.822 79.811 79.802 79.781 79.756 79.737 79.721 79.697 79.671 79.645 79.613 79.587 79.563 79.535 79.502 79.468 79.439 79.404 79.363 79.325 79.279 79.257 79.198 79.129 79.055 79.01 78.972 78.923 78.868 78.81 78.76 78.705 78.656 78.612 78.563 78.507 78.446 78.374 78.319 78.267 78.209 78.141 78.083 78.021 77.968 77.899 77.848 77.771 77.706 77.637 77.576 77.51 77.443 77.365 77.301 77.233 77.156 77.082 77.022 76.947 76.886 76.825 76.763 76.683 76.607 76.544 76.477 76.416 76.337 76.267 76.192 76.126 76.055 75.983 75.919 75.855 75.794 75.724 75.662 75.595 75.527 75.463 75.4 75.341 75.278 75.214 75.153 75.098 75.034 74.979 74.932 74.871 74.808 74.753 74.706 74.654 74.61 74.564 74.52 74.466 74.43 74.385 74.344 74.3 74.253 74.222 74.184 74.152 74.124 74.094 74.073 74.036 74.004 73.969 73.941 73.932 73.914 73.892 73.863 73.844 73.828 73.812 73.781 73.758 73.746 73.74 73.734 73.731 73.728 73.72 73.696 73.696 73.683 73.694 73.688 73.682 73.673 73.682 73.696 73.691 73.693 73.699 73.696 73.694 73.702 73.715 73.715 73.722 73.726 73.735 73.741 73.752 73.763 73.783 73.786 73.79 73.796 73.804 73.815 73.822 73.834 73.847 73.859 73.879 73.894 73.894 73.905 73.918 73.921 73.917 73.926 73.937 73.938 73.938 73.944 73.949 73.94 73.943 73.949 73.943 73.946 73.943 73.941 73.934 73.926 73.911 73.883 73.873 73.862 73.854 73.844 73.818 73.793 73.775 73.749 73.722 73.697 73.665 73.636 73.604 73.566 73.534 73.5 73.462 73.413 73.366 73.323 73.273 73.224 73.174 73.133 73.085 73.032 72.982 72.92 72.852 72.788 72.714 72.661 72.605 72.539 72.47 72.397 72.327 72.241 72.167 72.096 72.019 71.939 71.855 71.779 71.704 71.637 71.547 71.466 71.366 71.3 71.211 71.125 71.045 70.97 70.891 70.801 70.711 70.616 70.531 70.449 70.363 70.262 70.186 70.105 70.027 69.953 69.875 69.777 69.705 69.637 69.556 69.48 69.403 69.322 69.255 69.194 69.124 69.049 68.967 68.892 68.836 68.766 68.695 68.636 68.578 68.529 68.476 68.418 68.364 68.294 68.241 68.192 68.146 68.102 68.042 67.995 67.946 67.893 67.859 67.832 67.797 67.74 67.691 67.65 67.597 67.568 67.545 67.511 67.49 67.476 67.417 67.38 67.356 67.32 67.287 67.25 67.212 67.186 67.136 67.115 67.086 67.053 66.995 66.963 66.93 66.88 66.825 66.808 66.779 66.732 66.66 66.606 66.571 66.541 66.484 66.42 66.344 66.297 66.242 66.175 66.101 66.016 65.927 65.865 65.805 65.755 65.654 65.578 65.497 65.418 65.317 65.213 65.128 65.021 64.957 64.853 64.73 64.611 64.511 64.4 64.29 64.17 64.072 63.973 63.832 63.709 63.581 63.466 63.353 63.22 63.088 62.935 62.851 62.717 62.621 62.482 62.335 62.18 62.01 61.873 61.742 61.624 61.502 61.368 61.223 61.107 60.962 60.81 60.666 60.549 60.427 60.301 60.15 60.012 59.844 59.717 59.537 59.4 59.233 59.078 58.963 58.831 58.657 58.498 58.367 58.226 58.034 57.851 57.688 57.558 57.364 57.17 57.053 56.871 56.656 56.426 56.252 56.06 55.852 55.663 55.475 55.258 55.013 54.819 54.537 54.303 53.955 53.629 53.452 53.26 53.017 52.768 52.5 52.205 51.891 51.627 51.313 51.015 50.666 50.336 50.029 49.668 49.323 49.01 48.615 48.239 47.873 47.481 47.042 46.646 46.259 45.874 45.465 45.018 44.564 44.115 43.666 43.216 42.705 42.208 41.768 41.216 40.645 40.109 39.614 39.073 38.51 37.941 37.337 36.751 36.174 35.546 34.979 34.326 33.736 33.129 32.514 31.803 31.108 30.423 29.741 29.03 28.386 27.687 26.949 26.296 25.562 24.842 24.246 23.598 22.957 22.202 21.48 20.891 20.351 19.669 19.176 18.537 17.99 17.447 16.904 16.268 15.718 15.364 14.812 14.347 14.092 13.964 13.433 12.92 12.43 12.279 11.203 11.913 10.845 10.956 10.414 9.578 9.291 9.26 8.702 8.41869 7.43974 7.41869 6.43974 5.62021 3.14214 2.15569];
xmax=[900 721 546 444.5 386.5];
ymax=[81.111 85.099 79.802 73.413 66.484];
xmin=[845.5 620.5 493 412];
ymin=[79.415 77.402 74.124 68.636];
plot(x,y,'-k',xmax,ymax,'--b',xmin,ymin,'--r');
yL = get(gca,'YLim');
line([723.5 723.5],yL,'Color','g');
line([552.5 552.5],yL,'Color','g');

Respuesta aceptada

John D'Errico
John D'Errico el 11 de Nov. de 2019
The red curve is a piecewise linear interpolation, not really a curve, just connect the dots by the plotting routine.
The green lines are just vertical lines, so a fixed value of x. So all you are asking is how to use linear interpolation. You can find both solutions at once. interp1 will do it for you.
yred = interp1(xmin,ymin,[552.5, 723.5],'linear')
yred =
75.654 78.324

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