这里涉及到的是定语从句的简化概念 .简化为 分词短语,而到底是现在分词(也就是ING形式)还是过去分词要根据 被修饰的那个词(或者从句里的关系代词)是作主动还是被动.
1 首先来看做主动的情况,也就是简化为现在分词ing形式
关系代词所引导的定语从句为限制性修饰（关系代词前无逗号）,且该关系代词在从句中为主语时,可将从句简化为分词短语,方法如下：
第一步：删除关系代词；
第二步：将关系代词后的动词变为现在分词；
第三步：若动词是be动词,变成分词being后省略.
eg.The girl who lives next to my house is my classmate.
=The girl living next to my house is my classmate.
John is a young boy who is full of energy.
= John is a young boy (这里的being 是被省略的)full of energy.
(可以看出,提问者给的句子里的两处简化都是属于此种情况---即简化为 现在分词ing的形式
这是为什么呢?我们在带入作详细分析:
第一处 a cartoon 一部卡通片showing讲述的是一个...这里cartoon是作为show的主动关系,所以就是which was showing 然后省略which was而得到了showing,
第二处.讲述的是一个总统 怎样的总统呢>?一个拒绝射击小熊的总统,所以这里的定语从句时the president who refused to shoot a cute bear 而president 与refuse的关系很好判断,不是总统被拒绝何时总统自己主动拒绝,所以去掉who 将关系代词who后面的动词refused变成现在分词refusing 而得到了president refusing to shoot a cute bear
2 再看看做被动的情况,也就是简化为过去分词的形式
如果被修饰词与后面 修饰它的从句为被动的逻辑关系 如(被修饰的)book 被作者写,后面的从句省去which was之后就接的是written (被修饰的)car 被人开 后面的从句省去which was之后是driven
Have you ever read the book which was written by that author
=Have you ever been read the book written by that author
This is the car which was driven by my brother in the race.
= This is the car driven by my brother in the race .