Modify shortcode to work with custom taxonomies and slugs

I am using this code which works fine with posts but I am looking to modify it so that the user can specify in the shortcode:

• custom post type name


• taxonomy name


• slug of taxonomy category

Any ideas?

   function shortcode_latest_from_blog($atts, $content = null) {
        $sliderrandomid = rand();
        extract(shortcode_atts(array(
            "post_type" => 'post',
            "posts" => '8',
            "columns" => '4',
            "category" => '',
            "style" => 'text-normal',
            "image_height" => 'auto',
            "show_date" => 'true',
            "excerpt" => 'true',
        ), $atts));
        ob_start();
        ?>

            <div class="row column-slider">
                <div id="slider_<?php echo $sliderrandomid ?>" class="iosSlider blog-posts <?php if($style  == 'text-overlay') { ?>slider-center-arrows<?php } ?>" style="min-height:<?php echo $image_height; ?>;height:<?php echo $image_height; ?>;">
                    <ul class="slider large-block-grid-<?php echo $columns ?> small-block-grid-2">

                        <?php
                        $args = array(
                            'post_status' => 'publish',
                            'post_type' => $post_type,
                            'category_name' => $category,
                            'posts_per_page' => $posts
                        );

                        $recentPosts = new WP_Query( $args );

                        if ( $recentPosts->have_posts() ) : ?>

                            <?php while ( $recentPosts->have_posts() ) : $recentPosts->the_post(); ?>

//truncated..